Ruddy is due to leave Norwich when his contract expires at the end of next month, as he was part of a raft of first-team players released by new sporting director Stuart Webber.
West Ham have struggled to find a consistent number one this season and could look to Ruddy to fill that void for next season.
Ryan Bennnett, Youssouf Mulumbu, Kyle Lafferty Steven Whittaker, Michael Turner and Sebastien Bassong are also set to be let go by the club.
Bennett has already been touted with a move back up to the Premier League, with former Norwich manager Chris Hughton – at Brighton – keen on his signature.
The report also claims that Norwich are looking to offload Graham Dorrans and Steven Naismith – who scored a combined 13 goals for Norwich from midfield this season.