Wilshere looks set to be included in Fabio Capello's Three Lions squad for next Wednesday's friendly against Hungary having been left out of the under-21s by Stuart Pearce.
The 18-year-old impressed after joining Bolton on loan in January and Coyle has been keen to re-sign Wilshere for the 2010-11 campaign.
That prospect seems unlikely after Arsene Wenger indicated at the weekend that he would give the youngster a chance to stake a claim for first-team action this term.
Wenger also highlighted Wilshere's international credentials, something Coyle - who refuses to give up his pursuit entirely - believes have been enhanced by the spell the player had with Bolton.
"It's well documented that we would like to have him back for another six months," Coyle said.
"I have to say it looks like Arsenal are going to keep a hold of him, and you can understand why.
"He is absolutely quality and I'm led to believe that there is a chance he could be in the England squad.
"If he is, then it will be merited, it will be just, it will be a great reward for him and I think the football club will realise we have played a little part in that.
"I've always left the door open with Arsenal and Arsene, saying that if he felt after the season starts that Jack is not going to start games, then we would welcome him with open arms for six months and hopefully give him back in January a far batter player than what we got - because we already did that."
One international Coyle has brought back to the club is Croatia striker Ivan Klasnic, who scored eight goals for Wanderers while on loan last season.
Klasnic signed a two-year deal at the Reebok Stadium earlier this week after having his contract terminated at Nantes and Coyle revealed the player had turned down more lucrative offers to seal his return.
"The guy has had a glittering career and he could have very easily gone elsewhere for far better finance," Coyle said.
"Only on Saturday morning I had a phonecall from Roy Aitken at (Dubai-based club) Al Ahli and they were going to offer him the world.
"Ivan knew that, but he knew that he wanted to come and play for me.
"We had to put a deal in place that he was comfortable with and it is nowhere near the deal he had at Nantes, but it was within our budget and we managed to get it through.
"Bringing him in on our wage structure was a great piece of business and I'm sure he will reward the fans with goals."
Coyle has been linked with Oldham striker Tom Eaves, who netted a hat-trick against Wanderers in a pre-season friendly last month.
"The young lad in question has a terrific talent," Coyle said. "I was actually aware of him before the game and then that cemented what we already knew.
"There are a number of young players out there that we have made an inquiry about or have an interest in, and it would be remiss of me to start talking about individuals.
"But it's fair to say that he is a young lad with talent and has a chance in the game."