A pounds 2m lottery application submitted by the RSC seeks money to explore options for redevelopment.
No mention is made of replacing the theatre in its entirety. But The Independent has learnt that the RSC director, Adrian Noble, has begun talks with the Dutch architect Erick Van Egeraat on the construction of a new theatre.
The Royal Shakespeare is steeped in tradition. Leading actors of every generation have appeared there. Many seminal productions, such as Sir Peter Hall's Wars of the Roses, had their first performances on the RSC stage.
Recently, landmark productions have been fewer, though the late Sir Robert Stephens's career was resurrected when he was cast by Adrian Noble to play King Lear in 1993.
His performance illuminated the stage and won awards.
The theatre also has a unique architectural history. Its architect, Elisabeth Scott, was the first woman to design a theatre. The 1932 Art Deco building was designed to resemble an ocean liner when viewed from the other side of the Avon, and it still does, particularly when lit up at night.
It has splendid views over the river with an atmospheric coffee bar and terrace on the water's edge.
But in recent years the 1,500-seat theatre has been increasingly unpopular with directors, actors and audiences, who all prefer the smaller mock Elizabethan Swan Theatre next door. One performance of Twelfth Night at the main theatre earlier this year was a staggering 90 per cent empty.
Ian Rowley, an RSC spokesman, confirmed last night that Mr Noble plans to demolish the theatre, though the inside of the Grade II listed foyer would probably remain. But the famous riverside "ocean liner" effect of the theatre would be altered for ever.
Mr Rowley said: "There are numerous problems with the building. It's austere and very unwelcoming. The most exciting and most pragmatic thing for us to do would be to create a new theatre, a more egalitarian space where every seat in the house has good acoustics and good sightlines.
"At present the theatre is too big, the stage and auditorium are all wrong, and the balcony, which contains a third of the audience, starts at the back of the stalls. You're miles away. No modern theatre would be built like that. Schoolchildren having their first experience of Shakespeare can't see or hear properly and they have to enter through a different door."
Mr Rowley added that a new theatre, which the company hopes to start building in the next five years, would be in the same prime spot by the river, but in addition to changes in the auditorium there would be better access to the riverside and a much bigger front of house with an information centre, meeting rooms and performance space.
Yesterday the actor David Calder, who is playing Prospero in The Tempest at the RST, said: "You try and get the voice up to the back of the gods here. It's very difficult. The relationship between the stage and the auditorium is poor, and backstage the most you can have is four separate people having separate dressing rooms and that can get on your nerves."
Clare Holman, who is playing Isabella in Measure For Measure, said: "It's a very difficult theatre to play. It's a declamatory theatre. The auditorium is not embracing. It's very square and it's difficult to receive an audience reaction. There should be a circle of communication, but there isn't."
Mr Rowley said yesterday that the architect, who has built the Natural History Museum in Rotterdam and is also designing a new Photographers' Gallery in London, would ensure that the new theatre would blend in with the local environment. Mr Van Egeraat tends to work with glass and natural materials.
The present building replaced the Shakespeare memorial Theatre, a Victorian gothic building, which burnt down in 1926. Every decade has seen the finest performers of their generation star in the RST - Donald Wolfit, Paul Scofield, Peggy Ashcroft, John Gielgud, Laurence Olivier, Michael Redgrave, Richard Burton, Judi Dench, Ian McKellen, Diana Rigg, Helen Mirren and Kenneth Branagh.
Disaffection with the theatre building appears to be recent. It thrived in the Sixties and Seventies with productions such as Sir Peter Hall's Wars of the Roses with Peggy Ashcroftt, Ian Holm and David Warner, and Peter Brook's A Midsummer Night's Dream set in a white box with the fairy king making his entrance on a trapeze.
The RSC said yesterday that no rebuilding work was likely to start until after 2000, and the space occupied by the RST would definitely be again occupied by a theatre.
Dame Peggy Ashcroft
A mentor and role model for younger actresses, Dame Peggy was a definitive Queen Margaret in Sir Peter Hall's The Wars of The Roses, among other roles
Sir Peter Hall
Created the Royal Shakespeare Company in 1960. Among those whose careers he guided in the Sixties are Judi Dench, David Warner and Diana Rigg
Played Othello opposite Peggy Ashcroft's Desdemona. The sexual electricity between Robeson and Ashcroft was not confined to the stage.
Sir Laurence Olivier
Appeared at the Royal Shakespeare Theatre in the Fifties, most notably as Coriolanus and also as Macbeth, where he played opposite his then wife, Vivien Leigh, in 1955Reuse content