And the club reportedly want to loan the Tottenham Hotspur striker, despite a strained relationship with their north London rivals.
Indeed, the controversial striker appears to have no chance of staying with Tottenham this season and is said to be on West Ham's shortlist of potential new forwards.
The Daily Mail among others are reporting that Adebayor wants to remain in London, with that being one of the chief reasons he stalled on a potential deal with Aston Villa.
But the Mirror specifically suggest the Spurs man wants to join West Ham. Their report also suggests the Hammers are reciprocating the interest, with the club eyeing a loan bid despite their strained relationship with Tottenham after Adebayor's controversial failed move to Upton Park in January.
Can both clubs overcome their differences?
There appeared to be considerable fallout when the 31-year-old striker's attempt to join West Ham fell through thanks to Daniel Levy's decision to block it.
But the needs of both may work together perfectly to push a deal through in this case. Indeed, Tottenham are desperate to let Adebayor go - and the Hammers desperately need a new striker.
But would he be worth it?
The problem for West Ham, of course, is that they may have to settle for the 31-year-old due to a lack of available options. The east London side's 2-0 win at Arsenal demonstrated what Slaven Bilic wants from his players - hard graft.
Sadly, Adebayor doesn't fit that bill in any way. But the Tottenham forward might be West Ham's most practical solution.