The show, which has grossed more than pounds 1bn world-wide in ticket sales and merchandise, will beat the previous record of 6,137 performances held by the Broadway production of A Chorus Line.
Cats opened at the New London Theatre in Covent Garden on 11 May 1981 and has played to full houses since, earning pounds 85m in London alone.
The musical, based on TS Eliot's Old Possum's Book of Practical Cats, received mixed reviews when it opened but, with its revolving stage, was praised for pioneering new theatrical production values. Sue Uings, who was box office manager when Cats first opened and is now head of marketing for the theatrical impresario Sir Cameron Mackintosh, sees the technology as a key factor in the musical's success. "It was the forerunner of all the hi-tech musicals," she said.
Steven Wayne, the only member from the 1981 original cast still in the show, has not tired of hearing the Cats theme "Memory", "because everyone sings it differently. The only time it annoys me is when I am on holiday and I hear it piped in a hotel or on a plane".
However, the musical still has some way to go before it breaks the 44- year record of The Mousetrap, which is Britain's longest-running stage show.
8 Cats has been seen by 7 million people in London alone.
8 There are nine current productions playing around the world.
8 In 1989, it became London's longest-running musical.
8 Dame Judi Dench was due to play Grizabella but had to pull out just before the show because of an injured ankle. She was replaced by Elaine Paige, who sang the worldwide hit "Memory".
8 There have been more than 100 recorded versions of "Memory". Sheet music sales of the song in the UK total 95,500.Reuse content