At the moment there is nothing to suggest the Hammers are looking at bringing the cult figure back to the club for a third spell after he was released earlier this summer.
But after it was confirmed pacy Ecuadorian star Enner Valencia would miss the next three months with a lower leg injury sustained in the 2-2 Europa League draw with Astra Giurgiu the Hammers find themselves in a difficult situation.
Slaven Bilic's side have been linked with the likes of Queens Park Rangers forward Charlie Austin and Atletico Madrid's Raul Jimenez, as per the London Evening Standard but there is no indication any of those moves are in motion.
Were West Ham right to let Cole go before finding a replacement?
The club let Cole and Nene go over the summer and only brought back outcasts Mauro Zarate and Modibo Maiga into the fold after both were frozen out under Sam Allardyce.
While Zarate has shown he could be a useful player to have around this pre-season, Maiga has only reinforced that he has no future at the club with a string of woeful performances extending his miserable spell in east London.
And with the injury-prone Andy Carroll ruled out until at least September, it leaves just one senior proven Premier League performer up front for the Hammers in Diafra Sakho, who himself suffered with injuries which kept him out for two extended spells last season.
Valencia's injury has merely exacerbated a need that was already there ahead of what is one of the most important seasons in West Ham's history as they play their final campaign at their Boleyn Ground home of 112 years before moving to the 54,000 seater Olympic Stadium.
Still a free agent after being released this summer
So if the Hammers find themselves desperate come the close of the transfer window at the end of the month, is it that unthinkable they might re-sign Cole, who is still a free agent.
Rumoured targets like Jimenez have much worse goalscoring records than Cole who scored 57 goals in 259 appearances for the Hammers over nine years.
Carlton Cole: The making of a Hammers cult hero
Loved by Hammers fans for his great attitude and being a team player during his time in east London, Cole earned cult status when in September 2013, after West Ham failed with a number of bids for strikers at the end of the transfer window, he returned to the club to solve their perennial striker problems.
However, the move did not go through immediately due to concerns over his fitness following an uncertain summer period. After training at the club to regain his fitness he eventually signed a short-term contract and went on to score a handful of important goals earning him another 18 month deal in the January.
Then on deadline day in January this year, after being used sparingly by Sam Allardyce, the chance arose for Cole to join Tony Pulis at West Bromich Albion.
However, when West Ham's own move for Tottenham Hotspur's Emmanuel Adebayor was vetoed by Spurs chairman Daniel Levy at the 11th hour Cole was recalled yet again, much to the striker's chagrin.
He was quickly back to focusing on West Ham but again was barely used by Allardyce as both manager and player were released at the end of the season.
Given West Ham's need, the lack of options available within the club's budget and his affiliation with the club, would it be that absurd to see him back in the claret and blue again?