Bidders including TDR Capital have offered £850m for the company, which is below the £1bn price tag, said the Telegraph.
Other suitors include Chinese private equity firms Citic Capital Partners and Hony Capital and Chinese conglomerate Fosun.
Hony and TDR could team up to make a joint bid for the company, sources told the publication.
Pizza Express is expected to kick off exclusive talks with its preferred bidder next week.
Private equity firms TPG and Advent International have also expressed interest in the chain but have pulled out of the auction process.
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