United are unbeaten in their last four Premier League games and stunned Juventus with a 2-1 win in Turin in the Champions League on Wednesday.
Jose Mourinho’s side have become second-half specialists and have come from behind to claim points four times in the last month.
Sky Sports presenter Jeff Stelling suggested to Thompson United are returning to how they were under Sir Alex Ferguson, where they became known for scoring late goals.
“Late win against Bournemouth, late win in Juventus,” Stelling said.
“They’re beginning to resemble the old Manchester United aren’t they?
“In the way they play right until the last minute.”
And Liverpool hero Thompson, who won 22 trophies in a 13-year career at Anfield, admitted he was concerned at how United have started to turn it around.
“It’s worrying for everybody isn’t it that they’re finding that,” he said.
“People have been talking about their mojo in midweek.
“Maybe in the right circumstances Manchester United are finding it.”
However, Thompson reckons United cannot rely on coming from behind every game.
He says Mourinho must find a way of getting his team to start matches faster.
“But I always come back to saying it, when you’re 1-0 or 2-0 down it’s a lot easier to play because your shackles are off – ‘now we can start playing’,” Thompson continued.
“And this is the way it seems with Manchester United.
“Jose has got to find that formula of getting them to start quick and being more on the front foot, rather than losing a goal and ‘oh my goodness, now we’ve got to be more adventurous’.”
United return to Premier League action on Sunday when they visit local rivals Manchester City (4.30pm).