The sale would still leave Lloyd Webber, 56, as the owner of seven larger theatres - the Palladium, Theatre Royal Drury Lane, the Cambridge, Her Majesty's, the Palace, New London and the Adelphi, reported The Guardian.
A mystery buyer, believed to be American, has approached Lloyd Webber hoping to buy four of his smaller playhouses.
Five years ago the composer, now one of West End's biggest landlords, had masterminded a 90 million pounds deal to acquire 10 theatres from the Stoll Moss group.
The West End's two other major theatre owners are Cameron Mackintosh, who owns seven, and the Ambassador Theatre Group, which owns 10.
Despite an estimated 400 million pounds fortune, including an art collection believed to be worth 200 million pounds, Lloyd Webber has, in recent times, mourned his lack of financial acumen.
Lloyd-Webber has dominated British musical theatre for 30 years with productions such as "Joseph and The Amazing Technicolor Dreamcoat", "Cats", "The Woman in White" and "The Phantom of the Opera".