Cole left West Ham in July after failing to agree a new contract with Sam Allardyce's men.
Allardyce was reportedly eager to boost his attack in the transfer window, with Juventus' Fabio Quagliarella among the players to be linked with a move to Upton Park.
West Ham signed Andy Carroll from Liverpool in June following the former Newcastle United striker's successful loan spell last season, however, the England international has yet to feature this term because of a heel injury.
The London club's inability to add another forward to their ranks appears to have forced them to turn to Cole, who was unable to find a club despite reported interest from Crystal Palace.
"The club are pleased to announce that popular striker Carlton Cole is also undergoing a medical today (Tuesday) with a view to returning to the Boleyn Ground on a short-term deal," a West Ham statement read.
Cole joined West Ham in 2006, moving from Chelsea after loan spells with Wolves, Charlton Athletic and Aston Villa.
The 29-year-old made 237 appearances for West Ham, scoring 59 goals.
