The right-back is aiming to oust Bacary Sagna from Arsene Wenger's first-choice XI, which he believes would put him in the frame for a place in England's World Cup squad.
Jenkinson was signed from Charlton two years ago and turned in some impressive performances when Sagna was injured.
He signed a new, improved contract with the Gunners last November, and now he wants to establish himself as a first-team regular.
"It would be a dream for me to go to a World Cup and if I can play for Arsenal every week then I would give myself a chance," he said. "But that's a big target for me.
"It's a big season for me. I look at it as a massive season. I've had a couple of years now where I've played, settled in and personally I've raised my level and got more chances.
"Hopefully I'll get more playing time than I did last year because that was a bit frustrating at times but I think this is an opportunity to show I'm ready.
"If I can play in some of these games then I think I can show that I can play week-in and week-out.
"Bacary finished up playing every week last season. Most people would say he's first choice. He's a fantastic player and has been for many years. I've got the utmost respect for him.
"But he knows I want to push him for his place. I hope I can push on to the next level and ultimately take his place and play every week."
Jenkinson made his England debut against Sweden in November and he is hoping national boss Roy Hodgson has him in mind for a place in the squad for Brazil next year.
"The England call-up gave me a lot of confidence. Having the faith of Arsene Wenger is one of the biggest things in football and then getting a call-up from Roy Hodgson for England was massive for me," he said.
"I like to think that I'm still in his plans. But he doesn't pick many players who aren't playing regularly so that's got to be the challenge to me.
"Everyone wants to play in the World Cup. That's the pinnacle. As a player you feel a bit more pressure, because it's so important for any player. It's a huge year for me."