HITC Sport understands that Slaven Bilic's side are hoping to land the Atletico Madrid forward on loan.
The 24-year-old only joined Atletico last summer when they paid Club America £10million for his services, and he signed a six-year deal.
Jimenez started 21 games for Diego Simeone’s side last season and although popular with the manager, it is understood that Atletico are open to offers.
Portuguese giants Porto and Benfica are both ready to offer him first-team football, but West Ham are also in contention.
HITC Sport understands that West Ham want to take Jimenez on loan with a view to a permanent deal – and although Atletico would ideally prefer a cash bid, they are set to allow the player to make his choice.
West Ham are looking for high calibre additions and Slaven Bilic is a big fan of Jimenez, who he feels could be well suited to the Premier League.
The Hammers are still in talks with Alex Song over his return to the club, but the fact the Cameroonian is demanding a three-year deal could see West Ham look elsewhere and HITC Sport understands that they have a target in mind – should the former Arsenal man not sign.