Jenkinson has been on loan at West Ham this campaign, and faces an uncertain future at Arsenal.
Liverpool may want Jenkinson to replace the outgoing Glen Johnson, but any approach is doomed to failure.
The defender is an England under-21 international and Arsenal will not just want to let him leave on a whim.
West Ham may stand a chance of convincing them to let the right-back depart, because they have already had him for a season, and they are not considered a direct rival for Arsenal.
It is for this reason that Arsene Wenger will not allow Jenkinson to join Liverpool, for he is a player whose best years are ahead of him, and could conceivably fill a spot at right-back for the best part of a decade for a club who are likely to be battling them for seasons to come.
Doubt remains over the 23-year-old's future due to the competition for his place at Arsenal thanks to Mathieu Debuchy, Hector Bellerin and Calum Chambers.
Yet after the short shrift Liverpool gave them when they attempted to sign Luis Suarez in 2013, Arsenal are unlikely to let Jenkinson make such a switch unless a spectacular bid is forthcoming.