Sagna is widely expected to move to pastures new when his Arsenal contract expires at the end of next month, with Premier League champions Manchester City reported to be interested in his services.
And Jenkinson, who made 22 appearances in all competitions last season, is confident he can fill the void if Sagna does choose to depart.
"I feel that I am ready for it (starting at right-back)," Jenkinson told the London 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.
"I am the sort of player who needs to play regularly to get the best out of me. My fitness and my athleticism is a big part of my game, getting up and down the pitch.
"It is difficult to show what I can do when I am not playing regularly because it is hard to get into a rhythm."
Jenkinson has been linked with a loan move away from the Emirates Stadium, but is determined to stay at Arsenal and fight for a regular place.
"As far as I am concerned, you will have to drag me out of this club before I leave," he added. "I will work my socks off and hopefully next season can be a big one for me.
"If I have a good pre-season, work my way into the team and get a good run of games, there will be no holding me back."
