The England international defender has been a revelation at Upton Park this season since leaving the Gunners on loan in search of more game time.
It has certainly paid off for the 23-year-old who, but for his loan status, would be a serious contender for the East Londoners' Hammer of the Year award.
Though yet to score in the claret and blue, Harlow born Jenkinson's barnstorming runs and crossing down the right have been a real feature of the team's season. That coupled with his tireless efforts at both ends of the pitch - who can forget that brilliant last ditch tackle on Chelsea's Diego Costa at Upton Park - have endeared him to the club's fans.
He is reportedly valued between £8-10 million by the Gunners. And his reputation was only enhanced at the weekend when during West Ham's stalemate at Queens Park Rangers, Jenkinson became the joint fastest player on record this season, according to the Premier League.
The Irons spent much of a drab London derby defending but Jenkinson stole the show when he clocked up a top speed of 35.3 kilometres per hour to match a season's best record set by Newcastle United midfield powerhouse Moussa Sissoko.
While West Ham have struggled since Christmas, Jenkinson's personal performances have not suffered and he has always maintained the highest of standards.
In fact he has been so good for West Ham that the club now faces stiff competition from across the Premier League and Europe for his signature should, as expected due to the emergence of the likes of Hector Bellerin at his parent club, Jenkinson leave North London in the summer.
The truth is Arsene Wenger has an embarrassment of riches in the full back position and Jenkinson knows he will be one of the first names on the teamsheet at the Boleyn.
There is also the added carrot for Jenkinson that he is able to stay in London and has the prospect of playing in the iconic Olympic Stadium the season after next.
Earlier this month the boyhood Gunners fan admitted his future is 'in Arsenal's hands' when speaking to The International Business Times. He said: "I've got to focus on my football for the time being and then things will look after themselves.
"But West Ham has been perfect for me, and I've loved every minute. It's definitely a place I'd consider staying, but the ball is in Arsenal's court. I've enjoyed my time at West Ham. I also want to play at the highest level I can.
"I've got a massive summer in front of me at the U21 European Championships, so my focus isn't really on where I'm going to be next season."
Pace is a precious and expensive commodity in the Premier League. With those Championships looming for Jenkinson the Hammers know they will have to act fast to tie up a deal for a player who still has his best years ahead of him.