With just ten games remaining, Louis van Gaal's men are two points above Liverpool in fourth, but have a tough-looking run in between now and the end of the campaign.
The Gunners, meanwhile, have the best home form in the division as they surge up the table and are now only one point behind second-placed Manchester City after their defeat to Burnley this weekend.
"If I was still playing for Arsenal, I'd be in the dressing room thinking; look guys we can still win the league title," the French legend said.
The Red Devils go into their match against Tottenham this Sunday in disarray amid criticism of Van Gaal's management credentials.
"People keep telling me that this Manchester United team is about to click," he added.
"After 28 Premier League games, I'm still waiting. And time is now running out for everything to fall into place for Louis van Gaal."
Should they miss out on a top four spot, the Old Trafford club will go without Champions League football for the second season in a row.
Arsenal, on the other hand, have a fight on their hands to stay in the competition themselves after losing the first leg of their tie against Monaco 3-1.
Henry told the Sun on Sunday: "Paris Saint-Germain and Schalke both pulled off shock results in the Champions League. PSG stunned Chelsea while Schalke gave Real Madrid a fright with their away win.
"And I believe Arsenal can do the same at Monaco on Tuesday. People will say I'm biased, I know, but despite trailing 3-1 from the first leg, my former club can produce a big result in the big game.
"It won't be easy, of course. Yet with the right commitment, Arsene Wenger's team can deliver a performance they will never, ever forget."Reuse content