Arsenal's Jack Wilshere
The 25-year-old spent all of last season on loan with the Cherries, who were previously the bookies' favourites to obtain his signature.
Wilshere has endured a nightmare over the last three seasons, as far as his fitness is concerned, making just 32 Premier League starts, with 22 of those coming last term for Eddie Howe's men.
He is incredibly talented, however, and still has a lot to offer at the very highest level, if he can remain fit for the entirety of the season of course.
An SkyBET have slashed the odds on the London Stadium being the England international's next permanent home, making them the 2/1 favourites to sign the Arsenal star, ahead of Bournemouth at 8/1.
Arsenal's Jack Wilshere in action
Wilshere would be a fantastic signing for the Hammers, what with his exceptional technique, and wonderful vision when in possession of the football.
There will be plenty of West Ham fans against the idea of bringing the 25-year-old to the club this summer though, what with his suspect injury record, but it could be the kind of risk that Slaven Bilic needs to take in order to take the club forward.
He has just one year remaining on his current deal, however, so Arsene Wenger might be tempted into selling the midfielder for a fairly reasonable price.
And who knows, bringing Wilshere to east London could turn out to be a real coup.
Arsenal's Jack Wilshere with manager Arsene Wenger