The Tottenham striker is keen on a London stay and Bilic tried bringing him to Lokomotiv Moscow and Besiktas.
The Togo international could have joined Aston Villa earlier in the summer, but his desire to remain in the capital thwarted such a move.
West Ham need a striker and would seem a viable option.
Also, they have a manager who has tried to sign Adebayor on two separate occasions.
Slaven Bilic left his post with Besiktas in Turkey this summer in order to make a move to London. In July 2013, as reported by the Daily Mail, Besiktas were keen to sign Adebayor from Tottenham after the striker had been frozen out by Andre Villas-Boas.
Bilic even said at the time:
"Adebayor is a very talented player, anyone would like him to be a part of their squad."
However, they were suspended from European football at the time and that proved a deal-breaker for Adebayor.
Bilic had tried before. In the previous summer, when manager of Lokomotiv Moscow, Bilic was keen on signing Adebayor from Manchester City – as reported by The Telegraph.
It is clear that Bilic is a big fan of Adebayor and with injury trouble to Enner Valencia and Andy Carroll he could be the perfect signing for The Hammers and Bilic could finally get his man.