Private equity group Cinven intends to hire banks within weeks with a view to selling or floating Gondola Holdings at some point next year.
Cinven and Gondola, which sold off the Byron burger chain to Hutton Collins earlier this month for £100m, declined to comment yesterday.
The company could be sold off or floated for around £1bn, the Sunday Times reported.
Cinven paid €1.34bn (£1.14bn) for the group in 2006, a year after Gondola listed on the London Stock Exchange with a market capitalisation of £431m.
Since the takeover, Cinven has pushed to expand Pizza Express internationally and, in April, installed Richard Hodgson as chief executive of the pizza chain.
Pizza Express now has 413 restaurants, having opened 16 last year, while Zizzi has 123 branches and Ask Italian has 216.
In 2012-13, Gondola posted sales up 3.9 per cent to £591.7m and earnings of £108.1m, down 5.6 per cent.