Unai Emery’s side are almost within touching distance of Spurs after a midweek of mixed fortunes for two near neighbours.
While Arsenal were able to crush Bournemouth 5-1 on Wednesday, Tottenham slipped to a 2-0 defeat away at Chelsea.
The gap between two old adversaries in the Premier League table is now down to just four points, with a meeting at Wembley next on the agenda.
Victory for the Gunners could allow them to harbour aspirations above and beyond merely securing a Champions League spot, but nobody at Emirates Stadium is getting carried away by lofty targets.
Jenkinson told reporters when asked if Emery’s side are looking higher than finishing fourth: “I think it’s a very easy thing to say but we’re looking at one game at a time.
“That’s the way we’ve got to look at things and it’s the way the manager looks at things.
“We just keep building. In the last few games in particular, we’ve played some really good stuff.
“We’re looking like a very strong side, which we are. We’ve got a lot of really talented players and we want to show that we can do well at the minute.
“Of course, we’ve got a tough game coming up but we’re going into it with a lot of momentum and a lot of confidence."
Arsenal have emerged victorious in five of their last six Premier League outings, finding form at a crucial stage of the season.
“It’s hugely important,” Jenkinson said on the need to continue stringing positive results together.
“Towards the end of the season is a very critical time because the competitions are coming to an end and it’s about being consistent to get the results.
“I think we’re doing that really well at the minute but we’ve got some big games coming up.
“It’s a very important time for us but as players, we all know that. Our focus is on doing a good job and doing what we need to do.”