The Futurist theatre, on the resort's seafront, was built in 1921 and still stages concerts, shows and films.
The building is in need of repair and the borough council set up a task group to discuss its future.
Proposals for a trust to run the building are to be considered by Scarborough Borough Council on Friday. The council bought the theatre in 1985.
A Â£100,000 subsidy was agreed by the council in November 2009, securing its future until at least the end of 2010, but the council said it may not be able to provide any more money.
In December 1963 the Beatles performed at The Futurist and stars who have trodden the boards at the 2,000-seat theatre since include Morecambe and Wise, Shirley Bassey and Ken Dodd.
Plans for the future of a 90-year-old theatre in Scarborough are being considered.