McLeish believes it is "ominous" that United have still to taste defeat despite not firing on all cylinders during the early part of the campaign.
He also feels the experience of his mentor at Aberdeen, Sir Alex Ferguson, will again be crucial and give United the upper hand during the run-in.
McLeish, whose side visit Old Trafford on Saturday, said: "I think it's ominous, the fact that they've got to this stage unbeaten and their form is probably gathering momentum.
"They are probably looking better now than in the earlier part of the season when they had a lot of draws.
"It's amazing that they are unbeaten and I think that they can only get better."