Jenkinson has impressed whilst on loan with the Hammers but the emergence of Hector Bellerin means his future with the Gunners is uncertain. Sam Allardyce is keen to make the deal permanent but he now faces some serious competition.
Brendan Rodgers is set to lose one of his homegrown stars in Glen Johnson this summer and Jenkinson would be a convenient replacement. The 23-year-old still qualifies as a homegrown player and would likely come a lot cheaper than Johnson's £110,000-a-week wages.
The same report rates Jenkinson at £7million but other reports have suggested Arsenal will be looking for closer to £10m for the 23-year-old. Wenger is well aware of the inflation that comes with homegrown stars and is keen to take advantage.
Jenkinson was sent on loan to West Ham at the beginning of the season after the arrival of both Mathieu Debuchy and Calum Chambers. Chambers has since played a more central role for the Gunners while Debuchy has spent most of the season out injured.
However, Bellerin has surprised everyone with his astronomical rise to the first-team. The 19-year-old has impressed with his attacking style and is tipped to sign a long-term contract soon.
Wenger recently suggested that Bellerin will not have an impact on Jenkinson's future at the club, suggesting he would bring him back once his loan spell ends. But it seems a good offer would tempt the Frenchman into selling.
Liverpool will be in need of a new right-back and Jenkinson has developed into a player that is capable of playing for one of the Premier League's top clubs. The Reds will have to convince Jenkinson to leave London, but the lure of European football should be enough.
Lure of the Hammers
But West Ham have a growing appeal for young English players. Their move to the Olympic Stadium and an increasing financial strength could give them the edge in a transfer battle.
Liverpool are certainly the bigger club, but West Ham could offer more assurances over first-team football as well as the chance to play in an iconic stadium.
Where should Carl Jenkinson go if given the choice between Liverpool and West Ham? Give us your opinion in the comment box below!
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