ALBANY, March 13— New York State officials, troubled by a decade of financial losses in the state's racing industry, are considering several proposals to reverse the trend and increase the state's diminishing share of racing revenues -including the possible abolition of the New York Racing Association.
They are concerned about the erosion on several fronts of New York State's position as the nation's leader in horse racing: the arrival of casino gambling in New Jersey, the increasing possibility of legalized sports betting, the popularity of offtrack betting and the failure of state government to help, a situation that some racing experts say has limited the industry's ability to remain competitive.
Innovative and aggressive action by other racing states, mainly New Jersey, Florida and California, has begun to siphon a greater share of racing dollars and racing jobs away from New York. For example, California tracks have introduced million-dollar purses to attract bettors, while New York has yet to do so. Nevertheless, more of what the racing industry considers its most prestigious thoroughbred races are held in New York than anywhere else.
Projections Pessimistic
The Racing Association and its operations have generated $50 million annually in direct revenues to the state and produced more than $1.5 billion in state parimutuel revenue since 1955, when it began operating the Aqueduct, Belmont and Saratoga tracks
By the Racing Association's own estimate, thoroughbred racing at the three tracks provides more than 10,000 jobs. The industry has contributed about $1 billion a year to the state's economy, both directly and indirectly, according to the association's tallies.
But state officials have long felt that New York was not making as much money as it could under the Racing Association. In addition, the association's recurrent indebtedness and inability to raise sufficient funds to cover capital construction costs have resulted in pessismistic projections that New York might soon derive no revenues at all from the association's tracks. Its debt increased from $29.4 million in 1979 to $32 million in 1980. 10-Year, $47 Million Loan
In the fall of 1955, the New York Racing Association, a group of horse owners and breeders, took a 10-year, $47 million loan from a consortium of banks to purchase four tracks, including the nowdefunct Jamaica Racetrack in Queens.
But because of the Racing Association's inability to pay its debts, the state has had to supplement the initial borrowing by providing temporary tax relief and allowing the association to permit races on any day except Christmas Day, Palm Sunday and Easter Sunday.
While some in the racing industry insist the outlook is not as bleak as many have forecast, the state's growing displeasure with the association has led some officials to consider a possible takeover of the Racing Association or a consolidation of all racing operations - on-track, off-track, and harness track.
Officials of the Racing Association insist that they are more competent than the state to run the tracks and need only state help. They want New York to issue $70 million in long-term, tax exempt bonds to help the association repay its current debt and make capital improvements at the tracks.
Legislative leaders have expressed concern about the soundness of floating $70 million in tax exempt bonds. Under the association's plan, the state would purchase the association's properties with the proceeds from the sale of the bonds and then lease the facilities back to N.Y.R.A. At the conclusion of the lease, the association would have the option of purchasing the facilities from the state for a nominal price.
''I detect no groundswell of enthusiasm for the state to shoulder the responsibility and risk of a substantial bond issue without the title to those properties reverting permanently to the people of the state,'' said Assemblyman William B. Finneran, Democrat of White Plains and co-chairman of the joint legislative task force studying the racing and breeding industry in the state. ''Support just isn't there for us to shoulder the risk, then for a nominal fee, return three modernized facilities to an association which is, for all purposes, like a private corporation.''
Mr. Finneran was appointed to the task force by Assembly Speaker Stanley Fink, Democrat of Brooklyn. Mr. Fink, who has taken a particular interst in the issue, has scheduled to hold a press conference tomorrow to present his own plan to resolve the state's racing problems.
The state could, for example, form a public benefit corporation, similar to that of the New Jersey Sports Authority, which operates the Meadowlands race track, a proposal which has been put forth by the task force. Such a proposal would provide the state with the option of either operating the facilities itself or leasing them to another operator. Doubts About State Takeover
But that, too, could have problems gaining support in Albany. Anthony Chetko, an aide to Governor Carey, expressed ''grevious doubt'' that the government was capable of running racing better that a private corporation.
And a spokesman for the Senate majority leader, Warren M. Anderson, Republican of Binghamton, said that Mr. Anderson had not tended to lean in the direction'' of a takeover, but quickly added that ''we can't rule it out.'' The spokesman, Richard Roth, noted that if there were a restructuring of the racing industry, the New York Racing Association ''may be taken out'' of the picture.
James P. Heffernan, president of the Racing Association, insists there is no risk to the state. He argues that the association is ''a solid company'' with considerable real estate to back any bonds floated in its behalf.
The association wants other help, such as a reduced state takeout - a move that encourages more business by giving more to the bettors. The takeout - the amount the state takes from bets - was reduced experimentally from 17 percent to 14 percent in 1978, with the state absorbing the loss. The results were good for the industry, but in a budget fight between Governor Carey and the Republican-controlled Senate, the 14 percent experiment failed to be extended the next year. Cuts in Attendance
Other plans to stimulate racing in New York have brought mixed results. Offtrack betting attracts new fans, but the association's members have long contended that off-track betting cuts into track attendance. While the association receives a share of the revenues from off-track betting, it gets a larger amount from track bets.
Bernard Rome, former chairman of the Offtrack Betting Corporation and one of the Racing Association's toughest critics, accused the association of holding back'' the growth of off-track betting even though the profits are returned to state and local governments.
''If it wasn't for off-track betting, N.Y.R.A. would be out of business,'' Mr. Rome said. ''But they are more concerned with preserving the tradition of racing at the track.''
Illustrations: photo of Aqueduct raceway photo of OTB office