The 28-year-old was signed from Bordeaux in 2007 by Alan Curbishley and, despite rarely living up to his £6million transfer fee, he secured a spell on loan with Real Madrid in 2009.
Norwegian striker Carew scored twice in 21 appearances this season after joining from Aston Villa at the start of the season.
Defender Faye and midfielder Diop also arrived on one-year contracts last summer.
Goalkeeper Rob Green is out of contract but the Hammers hope he can be persuaded to sign a new deal after securing promotion back to the Barclays Premier League.
Co-owner David Gold said: "There will be one on the table which should be acceptable and hopefully we will wrap that up in the next five weeks."
As he prepares for life back in the top flight next season, boss Sam Allardyce has also released striker Frank Nouble and young midfielder Olly Lee, the son of former Hammers and England star Rob Lee.