The 22-year-old right-back moved to the Hammers on loan from Arsenal this summer and he has enjoyed his time in his new surroundings so far.
The increased amount of first-team football has been a major positive for Jenkinson, but he has also praised the methods that Allardyce uses in training to help his players' development.
“He’s been absolutely brilliant,” Jenkinson told the Guardian. “I didn’t want to go on loan to a team that was just going to kick the ball long. I wanted to go to a team where I was going to learn and improve and I think I’m definitely doing that here at West Ham.
"We focus on defending in training and we do a lot of work on one-on-ones and heading and I feel I’ve developed in those areas. He’s given me the licence to get forward and express myself. I know what I’m capable of.”
Jenkinson has played 13 times for West Ham so far this season and his performances have impressed all viewers.
Blessed with masses of pace, the England international has been able to be a threat in attacking sense as well as being a solid defender.
West Ham are thought to be keen on making his loan move a permanent one, but Arsenal's reluctance to lose him in a cheap deal has put any long-term transfer on hold.
Jenkinson's future at the Gunners still looks limited though, with Mathieu Debuchy, Calum Chambers and Hector Bellerin all blocking his route to the first team back at his parent club.
For now, Jenkinson's focus will be solely on matters at West Ham and he will be looking to help them consolidate their place in the top four this weekend.
The Hammers face Leicester City on Saturday knowing that they have a good opportunity to collect three points and extend their advantage over the rest of the Champions League chasers.