The 21-year-old has started three of his side's opening four Premier League fixtures of the season, which have seen them collect nine points to sit second on the table.
Jenkinson faces tough competition at right-back at both club and international level, with Bacary Sagna at Arsenal and Liverpool's Glen Johnson and Kyle Walker of Tottenham battling it out for the England jersey in his position.
But the former Charlton Athletic man has already won one international cap by coming on as a substitute in last November's friendly defeat in Sweden, and feels he has what it takes to earn many more.
However, Jenkinson admitted that his top priority must be establishing himself in Arsene Wenger’s starting XI at the Emirates Stadium.
"I believe that if I am playing regularly, and I'm playing well, I can be England's right-back," he told talkSPORT.
"If you're going to break into the England squad you need to be playing regularly.
"First and foremost I need to show the boss what I can do and show my credentials and that I am capable of playing regularly at this club.
"I believe I'm getting to that stage now where I'm more than ready to take my place and play week-in and week-out at this club.
"It's up to me in training to show what I can do and when I get my chance I need to take it. It is important that I do that, especially in a World Cup year."
