Talksport radio presenter Geoff Peters claims West Ham have major interest in the 20-year-old alongside Bournemouth, Watford, Burnley and Celtic.
Norwich value the Northern Ireland defender at £10m and are about to offer him a new long-term deal.
Peters wrote on Twitter “Norwich have offered Jamal Lewis a new deal in light of major interest from Bournemouth and Watford. West Ham, Burnley and Celtic are also monitoring him. #ncfc value Lewis at £10m+ but the highly rated 20-year-old, capped by Northern Ireland, is in no rush to leave Carrow Road.”
The 20-year-old made his breakthrough with Norwich last season, making 24 appearances and establishing himself as first-choice at left-back under Daniel Farke, earning his first senior Northern Ireland cap.
Lewis signed a new contract in July 2017 committing to a deal until 2021, with the option for a further year.