The restaurateur has agreed heads of terms for a 4,500sq ft site in Soho and has identified two others of a similar size in the capital's theatre district and by the Thames.
None will be another Polpo, but rather a new style of restaurant, though Venetian and New York influences are likely to feature once again.
Although the deal for the Soho site is furthest along, it is expected to have the longest lead time - the restaurant isn't likely to open before 2014 as the building requires some demolition and rebuilding.
Norman also said he was planning to open a pizza restaurant in the capital following a recent 'fact-finding' tour of Brooklyn, in addition to the three sites previously mentioned.
"I have a strong urge to open a pizza restaurant. It won't reinvent the wheel, but there will be plenty to make people smile," he told Restaurant.
Norman and his business partner Richard Beatty currently own three restaurants under the Polpo name - in Soho, Covent Garden and Smithfield - as well as Mishkin's in Covent Garden and Spuntino in Soho. The pair are also looking for a new site for Polpetto since it was forced to move from The French House.
Read Russell Norman's updated Pearls of Wisdom in the December issue of Restaurant magazine, out now, or read our previous one from April last year here.