The Hammers are attempting to cut costs ahead of their first game back in the Championship, and Cole remains one of the players that could be moved on.
The 27-year-old said earlier this month he was "100% committed to West Ham" after talks with Stoke broke down over his wage demands, but he is still likely to be sold.
Stoke remain interested themselves and, according to Sky Sports, Sam Allardyce wants Carew, who spent the second half of last season on loan with the Potters, to replace Cole.
The powerful Norwegian is a free agent after his contract at Aston Villa expired at the end of the season.
Source: Team Talk
Source: Team Talk