United have started the season in impressive fashion, hammering Arsenal 8-2 in their last outing to make it three wins from the opening three fixtures of their Barclays Premier League title defence.
If they have looked uncertain in any position, it is in goal, where Spanish youngster De Gea, signed over the summer as a replacement for the retired Edwin van der Sar, has appeared to struggle at times.
The 20-year-old saved a penalty against the Gunners, though, and Coyle is certainly not thinking Bolton might have an easy task getting past him.
The Scot does, however, feel Wanderers - who led United twice at home last term in an eventual 2-2 draw - have it in them to pull off a victory when the two sides meet again at the Reebok Stadium on Saturday.
"David de Gea is a top goalkeeper - there is no doubt about it," Coyle said.
"With Manchester United, it is difficult to find any weaknesses, but my focus will be on making sure my group are at their best.
"We know as long as we get to our maximum that we can sleep well at night.
"What we don't want to do is be below that - it leaves that bad taste in your mouth, so I will be stressing to my group that we have to get to our best.
"If we do that, although we certainly won't be able to match Manchester United over the course of a season, on any given day we can win these games."
United's potency going forward is not in question, with their England duo Wayne Rooney and Ashley Young in superb form of late for both club and country.
Training with them on international duty over the past couple of weeks has been Bolton centre-back Gary Cahill - something which may set him in good stead for Saturday's match, although Coyle is confident the 25-year-old will have already known plenty about the threats Rooney and Young pose.
"I think he is well aware of their qualities - I don't think those days in England training will have made him any more aware of how good they are," Coyle said.
"It means there might be a little bit of banter, but Gary being the professional he is, he already knows everybody's strengths and weaknesses.
"There might be one or two things he has picked up at close hand, though. Who knows?"
Cahill played the full 90 minutes in each of England's recent Euro 2012 qualifiers, scoring his first international goal in last Friday's 3-0 win in Bulgaria, and Coyle can see the defender representing his country for the next decade.
"My belief is that he will have another 10 years of playing in that shirt," Coyle said.
"It was great to see him cementing himself in the team as opposed to going along and being a squad player. Gary did himself a lot of favours with his performances in both games."
Cahill is in the last year of his contract at Bolton and was strongly linked with some of the Premier League's biggest clubs over the summer.
No such transfer materialised, and while Coyle is sure it will come at some point, he has urged the player to focus on Wanderers for the time being.
"Gary is ambitious and wants to play at the highest level of the game," Coyle said.
"We are in the best league in the world but the next step after that is the Champions League, and I'm sure Gary would love in time to be part of an elite club.
"I think he's more than capable of playing for any of them and it will happen in time - I've got no doubts about it.
"I expected Gary would have gone this summer to an elite club because of the quality I know he has.
"It has not happened, and between us we have to make sure that Gary is doing what he has done to this point, which is playing ever so well for Bolton Wanderers."
Asked about talks over a new deal for Cahill, Coyle said: "I think they will happen, but you have to understand what is involved in it.
"When the transfer window closes, then you have a different set of circumstances.
"We will deal with it, as always, openly and honestly and take it from there.
"It is not a conversation for just now and at the end of the day, it will be between Gary and his representatives, who will have a bit of chatting to do I would imagine."