England striker Rooney has admitted he wants to leave United, due to the club’s lack of impact in the transfer market.
Coyle hopes the issue can be resolved and that Rooney decides to remain at Old Trafford.
“I truly hope that Wayne Rooney remains a Manchester United player,” Coyle said.
“I think we all accept that he is having an indifferent time in terms of his form, but it only takes one touch and finish for that confidence to go pumping through his veins again and for him to show his quality, because he is truly an outstanding player.
“I think Wayne Rooney and Manchester United are a tremendous fit and you don’t want the best players leaving the Premier League.
“If they can see it through, whatever the trouble is, and sort it out and he remains a Manchester United player, I will be delighted.
“I think everyone in football will be, because they are an unbelievable club, one if not the biggest club in world football and you don’t want to lose your best players – and he is certainly one of those.
“Sir Alex has seen teams change over the years and built teams up again and hopefully they can sit and have a bit of dialogue and sort it out.
“For me, Wayne Rooney and Manchester United go hand-in-hand, and you want that to continue and you want them to be strong.”
Coyle is confident United boss Sir Alex Ferguson will make sure the club will remain a force to be reckoned with.
He added: “Who am I to argue with one of, if not the best manager we have ever had?
“He has shown year after year that he knows that job inside out and how to get the best out of players. That will continue, and you will see this year again – Manchester United will be challenging for all honours because of the quality they have.
“Are they selective with the players they sign? Yes – and they are right to be so, because they try to get the cream. That is the type of player they have at the football club.
“There is no doubt that they will get it right.”