Jenkinson joined Birmingham City on-loan this week.
“My main ambition to play for England again," said Jenkinson, who could make his Blues debut at home to Reading on Saturday.
“That's something that's in the back of my mind and getting back playing this season is going to be a stepping stone towards that.
“I want to crack on and play at the highest level again.
“Whether that's at Arsenal or whether I end up moving on time will tell, but I'm not focusing too much past this season.
“I'd love to play for England again and in the back of my mind I really believe I can do that.
“But for the time being I've just got to focus on the short term and that's playing regularly here and hopefully I can push on from that."