The Blues won the tournament for the first time in their history in May by beating Bayern Munich on penalties.
The Gunners were losing finalists to Barcelona in 2006, but Jenkinson is adamant that the North Londoners have what it takes to go all the way in Europe's elite competition.
"If Chelsea can do it, then we can do it," Jenkinson told Arsenal Player. "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."
Arsenal host Olympiakos on Wednesday.