The 30-year-old began his career with the Hammers making his debut at 17, before moving to Chelsea where he won three Premier League titles.
He then moved to Liverpool in 2010 but struggled to make an impact at Anfield and has spent last season on loan in France.
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The report also claims that fellow ex-Hammer Nigel Reo-Coker is a potential target, after he left Bolton following the club’s relegation, but that his wage demands could make a deal difficult.
Other targets mentioned are left-winger Kieran Richardson, who played at youth level for West Ham and has 12 months remaining on his contract at Sunderland, and forward Victor Moses, who is understood to be available after declining to sign a new deal at Wigan.
The out-of-contract goalkeepers Manuel Almunia and Craig Gordon, along with Newcastle’s Fraser Forster who has been on-loan at Celtic, are named as potential replacements for Robert Green if the Euro 2012 squad member does not renew his deal which expires this summer.
In defence, Wolves’ centre back Roger Johnson and Crystal Palace right-back are also named as potential targets.
The reports of the potential new signings underline the value to the club of their 2-1 play-off final win against Blackpool
The Hammers were relegated last year and joint-chairman David Gold outlined the financial cost to the club had they failed to win promotion, commenting: “If we didn’t win then we would have needed to cut our cloth accordingly.
“We wouldn’t have sat there deluding ourselves. It would have cost probably around another £30m.”