The Gunners are five points behind Chelsea in fourth with 10 games left to play in the Premier League.
Jenkinson thinks that Arsenal can put the disappointment of defeat to Tottenham Hotspur behind them and catch their North London rivals in the league.
He told the club's official website: "There are two teams to chase and I don't think we can get too caught up in how they're doing.
"If we go on a good run now, we'll finish in the top four. I'm sure of that. If you look at Tottenham's run in, it's quite difficult. They've got some difficult games so we're going to hope that they drop points.
"If we focus on what we've got to do, I think it will take care of itself. It's in all the news [the run in]. It's on Sky Sports News so you can't really miss it. You see things like that and you would say that Tottenham have a more difficult run in than us."
Arsene Wenger's side face Bayern Munich on Wednesday before returning to domestic action against Swansea City next weekend.