Cole is available on a free transfer this summer, as his contract at Chelsea expires at the end of the season.
The England international is also being targeted by Manchester United, Tottenham and Arsenal.
Cole left West Ham in the summer of 2003 but has several times hinted that he would be open to a return to the club one day.
West Ham co-owners David Sullivan and David Gold believes Cole would be a great signing for the club, according to the Sunday Mirror.
