Louis van Gaal’s side need one point from their remaining two fixtures to ensure a return to the Champions League next year, which was arguably the Dutchman’s remit when he took over from David Moyes in the summer.
Jones, though, isn’t focusing on one point and is instead keen to take all three against Arsene Wenger’s men, helping to push the Red Devils on towards a potential third place finish.
"We need to make sure we beat Arsenal on Sunday," he said.
"It’s an important game, and we then have to hope that they drop some points in the last games of the season and we beat Hull as well. It’s our last game at home this season and we want to go out with a bang."
Of course, a third-placed finish would see whichever team achieves it avoiding a play-off game to qualify for the Champions League group stages, which any would be keen to do.
Aside from the Champions League, Manchester United are expected to strengthen in the summer, having already secured the signing of highly rated Dutch youngster Memphis Depay from PSV.
Should quality additions be made, and taking how the side has developed under Van Gaal this season into account, there are expectations from some that the Red Devils will challenge for the title in 2015/16, and Jones has admitted that is goal the Old Trafford playing staff will be setting themselves.
“I think the minimum we expected this season was to finish fourth but next season is going to be a big season for us," he added.
"We need to push on and certainly challenge for that title, there’s no reason why we can’t. Next season, we’ve got to hit the ground running, but we’ve got to finish this season off first and finish it off strongly.”