Jenkinson was sent on loan to Upton Park after being in and out of the Arsenal side for the past couple of seasons, but seems to be getting some regular football under Sam Allardyce at Upton Park after struggling with injury at the start of the season.
He told the West Ham website: "It has been positive and a great run for the team. We're unbeaten in five games so that's a good sign of where this Club's going, and personally it's the first time I've had a run of games in a couple of years now and I'm really happy with it.
"I'm really finding my feet and trying to contribute defensively and going forward as well.
"It was nice to keep a clean sheet on Saturday, I got an assist a couple of weeks ago and I want to add to that. I want to get as near to ten assists as I can this year. It's going to be tough but that's my aim."
With a deadly strike partnership up front in Enner Valencia and Diafra Sakho, who have made an impressive start to the season, if Jenkinson can provide the necessary deliveries, there is every chance he can get into double figures when it comes to assists this season.
So far, Jenkinson has the one assist to his name from his eight appearances in the Premier League this season but if Sakho and Valencia can keep finding the net - and given that they have been prolific at scoring from crosses - there is a chance he can hit his target this term.
In the same interview, Jenkinson said he is aiming to catch the eye of England boss Roy Hodgson whilst playing for the England under-21s.
He said: "It's a natural step from the Under-21s to the senior team and I feel like I'm getting there. I feel like there's an opportunity to get into the senior squad.
"I know I've got the ability to do it, I've just got to express myself and hopefully catch Roy Hodgson's eye."
The right-back position is seemingly up for grabs for the senior Three Lions side after Hodgson selected Nathaniel Clyne and Calum Chambers in his most recent squads to take up the role, so the England boss is certainly looking to the future in that position.
But he does face some stern competition if he wants to break into the senior side, but if he achieves his targets of assists with the club, combined with some impressive defensive displays, he may achieve both targets.