The Gunners right-back, 20, believes the Blues’ success in Europe last term shows anything is possible.
After defeating Montpellier in their first group B match, Arsenal face Olympiakos at the Emirates on Wednesday.
And Jenkinson said: “If Chelsea can do it, then we can do it. There’s nothing stopping us going all the way.
“We’ve just got to make sure we perform to how we can do in this competition and I believe if we do, we will progress.
“In this competition you’ve just got to take it game by game and just focus on it that way.
“I think that’s the best way to go about things.”