The Reds are currently seventh in the Premier League table ahead of Saturday's showdown at Anfield, seven points behind United who are joint top.
And former midfielder Ince, who also represented United during a distinguished playing career, believes they cannot afford to lose more ground if they are to stay in the hunt for the title.
He wrote in his column for Paddy Power: “Klopp hasn’t found the right formula for his team yet and, after this length of time at the club, with the players he has, he really should have.
“This game is United’s first acid test. They’ve been demolishing teams and, no disrespect to the others, but this is a big step up. To go to Anfield is different gravy, this is where they’ll truly be tested for the first time this season. United have to prove they really are title contenders.
“But Jurgen Klopp has more to prove than Jose Mourinho. If Liverpool lose, could you really class them as title contenders?
“At the minute, I can’t see it anyway. They’re way behind United and City and if they drop three more points here, they’re not going to make that gap up – no chance. It’s a huge game for Liverpool.
“If you look at the two sides at the minute, everything considered, you have to say United are way ahead of Liverpool.
“Win or lose, United will still be challenging for the title. Liverpool don’t come close.”
Ince believes that Mourinho will set his team up to push for three points at Anfield, with Liverpool having shown over recent weeks that they are vulnerable at the back.
He added: “Jose will want to win it. He can answer those doubters who are saying, ‘Well, they’ve not played anyone yet’. It’s a chance to shut people up.
“They’re scoring lots of goals, Romelu Lukaku is on fire, and that could really be the difference between the two teams. Liverpool don’t take chances and their defence is poor, you would think Lukaku would have too much for that back line.
“Man United at Anfield, against that back line, in the form they’re in now – they’ll score. There’s no doubt about it.
“There’s been a lot of unrest in Klopp’s side and United seem to know what they’re doing – that shows in the way that they’re playing.”