Jose Mourinho has been told to keep his cool
Mourinho is yet to beat his old side since being sacked halfway through last season.
They were beaten 4-0 at Stamford Bridge in the league and Mourinho appeared to lose his cool after Antonio Conte's celebrations.
Jose Mourinho and Antonio Conte clashed at Stamford Bridge in October
Jose Mourinho was unhappy with Antonio Conte's celebrations
Mourinho's side were also dumped out of the FA Cup at the Bridge in March.
But United are desperate for points on Sunday as they chase down a spot in the top four – and Mills thinks Mourinho needs to lead by example from the touchline.
"He has to take a lid on his emotions," the former England defender told told Premier League Daily.
"We want to see him fiery, revved up but he has to maintain it. If he gets too emotional and that transcends into the players then they will lose their focus and lose their concentration and that will cost them dear.
Manchester United v Chelsea combined XI Wed, April 12, 2017
Express Sport brings you our combined XI of Manchester United and Chelsea stars ahead of the Premier League clash at Old Trafford on Sunday (4pm)
Play slideshow Getty Images 1 of 13
Get Quotes on Home Insurance
Who makes our combined Manchester United and Chelsea XI?
"It's a very fine balance between the passion you need to go out and win a game like this and being too passionate, picking up red cards, making silly emotional decisions and making mistakes."
And Mills thinks the antics in the Premier League match, when Mourinho approached Conte on the sidelines, could have been pre-meditated.
"I am not sure whether that was deliberate," Mills added.
"Mourinho of old especially when he was at Chelsea in the good times and Inter Milan everything he did to me seemed premeditated.
"Whatever he said after a game, however he spoke, it was always to deflect away from his players, to put the attention and focus on him.
"Was that him doing the same because his players had a really big defeat that day, was he trying to take all the pressure and put it on himself? Possibly."