The Gunners, who thumped north London rivals Tottenham 5-2 in the Barclays Premier League this afternoon, trail Group B leaders Schalke by a point and are only one clear of third-placed Olympiacos heading into the final two European ties.
With Schalke entertaining Olympiacos, victory for both home sides would secure the top two slots and give Arsenal breathing space ahead of next month's trip to Athens.
Ramsey said: "The group is pretty tight at the moment, so yes I think you could say that we have to win this game, and we are at home so hopefully we can do that and put ourselves in a strong position to qualify.
"That is our aim and hopefully we can get the win which puts us in a better position.
"The ideal situation is that we will be qualified before going into the last game.
"Other matches are completely out of our hands, so we have got to look after our own results, but if Schalke do win, then that would be the preferred choice for us."
However, a Schalke victory would most likely leave Arsenal looking at second spot in the group, unless Montpellier were to do them a massive favour and turn over the Germans - who won 2-0 at Emirates Stadium last month - in France on Matchday Six.
In 2011, Arsenal finished runners-up to Shakhtar Donetsk and were handed a tough draw against Barcelona, going out to the eventual champions 4-3 on aggregate despite winning the first leg.
But Ramsey insists Arsenal should not fear anyone in the last 16, whether they are there as one of the top seeds or not.
"It (second place) has been quite costly in the last few years," the Wales international told Arsenal Media. "We finished second in the group a couple of seasons ago and played Barcelona, so you know you're going to have a strong team if you do finish second.
"But most importantly we need to qualify and if we do, we are confident that we can compete and challenge against any team in the competition."
Defeat for Montpellier would mean an early exit from Europe on their Champions League debut.
Arsenal recorded a hard-earned 2-1 win at La Mosson on Matchday One in September.
Ramsey is expecting the Ligue 1 side, whose only point so far came from a late 2-2 draw at Schalke, to provide a stern challenge on Wednesday night.
"When we played them in France we were under pressure for periods of the game and we did well to get a result there," he said.
"They have competed against every team and showed they can create and can be a threat, so it will be no pushover.
"Montpellier will want to prove something as well, that they can compete against the best teams, so we will have to be aware of that and be right on top of our game on the day."