United's next two matches are likely to have a significant bearing on the Reds' campaign.
On Tuesday, victory over Celtic would guarantee the Reds finish top of Group F, and so avoid the winners of the Champions League's other groups in the knockout stages.
Then, on Sunday, Chelsea visit Old Trafford, a game which, should United win, would see Sir Alex's side go six points clear of Jose Mourinho's men.
One player relishing both matches is Wayne Rooney, scorer of both goals in the 2-1 win over Sheffield United on Saturday. Beating the Blades sets the Reds up nicely going into a crucial week.
"It was a great win for us, especially with the Chelsea game coming up," said Rooney. "We are all looking forward to the Celtic and Chelsea matches and it was important we stayed three points ahead before the big game on Sunday.
"We had to show great courage and determination to come from behind against Sheffield United, but now we have to concentrate on Celtic. We have to do a job there and make sure we qualify for the next stage."
The good news is that, after scoring for England last week against Holland and then twice at the weekend, Rooney appears to be at full match sharpness.
"That's a great boost for me," he said. "Hopefully I can keep scoring, but we are also spreading the goals around."