The business, which is owned by Caird Capital and London & Regional, could sell for up to £900m despite concerns from some buyers the chain is overvalued, the Telegraph reported.
Both firms backed a buyout led by current chief executive Scott Lloyd, the heir to former English tennis professional David Lloyd who founded the chain, in 2007.
That deal saw £940m handed over to owner Whitbread just before the global financial crisis caused the value of many assets to plummet.
KSL Capital Partners are also said to be among firms putting the final touches to offers.
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