Sagna has been repeatedly linked with a move to Manchester City when his Gunners deal eventually expires this summer, and Jenkinson believes that it is now time for him to become a regular in Arsene Wenger's side.
"I feel that I am ready for it," the 22-year-old told the Evening Standard. "It is never going to be easy to nail down that spot but I believe in myself and I believe in my ability.
"I want that position to be mine for years to come. Of course I have got a long way to go, because this is a club who look for the best players in the world.
"If I am going to hold down the position for as long as I want to, I have got a lot of hard work on my hands. But I believe in myself."
Despite the recent reports, Sagna has insisted that he has not agreed a deal with City yet.