The Hammers are keen to sign a right-back this summer, with current full-back Guy Demel linked with an exit, and are interested in acquiring the 21-year-old Arsenal defender
The Hammers have already signed four players this summer and on Thursday announced they had agreed a deal for Ecuador's World Cup star Enner Valencia.
Sam Allardyce remains keen to strengthen his defence, despite the arrival of left-back Aaron Cresswell from Ipswich, and sources have confirmed that Jenkinson is one target “of many” for the club.
Arsenal acquired Mathieu Debuchy from Newcastle earlier this week and have also targeted a loan move for Atletico Madrid right-back Javi Manquillo, meaning Jenkinson will be allowed to leave on a short-term deal should Manquillo arrive at the Emirates Stadium.
The Irons are open to signing Jenkinson on a permanent deal but a short-term move appears more likely, given the player's age and potential.
Allardyce is keen to retain a British core at Upton Park and is also determined to drive the average age of the squad down, with the 22-year-old fitting the new-look recruitment profile at the club.
West Ham retain an interest in Manchester City right-back Micah Richards – who has fallen out of favour at the Premier League champions – while Guy Demel looks set to leave Upton Park.
Leicester have been linked with a move for the 33-year-old, while his former club Hamburg are also monitoring his situation ahead of a possible summer bid.