The pair joined the Trotters on loan during the January transfer window.
Both have been given opportunities to impress during their time at the Reebok Stadium, as they continue to learn their trade.
The playmaking duo have enjoyed their time with the Trotters, with Wilshere already admitting that he would welcome the opportunity to return next term.
Coyle is hoping an agreement can be reached which will allow both men to head back to the North West in 2010/11, and admits he is hoping to talk with Arsenal and City over the summer.
He said: "I would love to keep them because they know how I want to go about it. When the season finishes I'll speak to their respective clubs.
"I accept that Man City won't be as pleased with Vlad's time here as Arsenal will be with Jack's, because Jack has had more opportunities.
"I like ball-players. I accept that there are other attributes you need but it's fair to say that if you see the types of players I've brought in at my previous clubs, they're the sort of players I look to add to what we already have here.
"Vlad is confident. He wants to play, he knows he can play and my job is to make sure that he feels a big part of it.
"It's not just about the 11, it's about the whole group, that's where your strength is. I keep him involved and he knows, given the opportunity, I'll have him out there playing. Who's to say he won't be starting next week?"