The 34-year-old has been a free agent since August after leaving Indonesian side Persib Bandung, where he lasted less than half a year following spells with American side Sacramento Republic and Celtic.
Cole is refusing to hang up his boots as he looks to extend his career, in what could be a move to a Football League club despite West Ham fans urging him to rejoin the Hammers last month after he posted a tweet.
The former Chelsea striker claimed on Instagram that "there is still life in the old dog yet" as well as thanking Neil Eardley's side for allowing him to train with the club. It remains to be seen if Wimbledon are interested.
Cole joined the Hammers from Chelsea in 2006 and made a total of 293 appearances for the Hammers throughout his time at Upton Park, having a hand in 100 goals with 33 of those coming as assists.
It remains to be seen where the veteran will end up, but at 34 years of age he could still have a couple of years left in his career if he is willing to drop down into the third or fourth tiers of English football.