Elmander scored his side's second at Molineux, twisting and turning through a crowd of defenders just after the hour mark and coolly slotting home.
The Sweden international, who now has six goals this season, is out of contract in the summer and has been linked with a move away from Bolton, particularly after chairman Phil Gartside indicated the Trotters might be forced to sell to balance the books.
However, Coyle says he is content with the way talks with the player about a new deal are progressing.
"He is in the last year of his contract and he is well within his rights to let that run its course if he so deems," Coyle said.
"But I speak to him every day on the training ground and we have a very good relationship. I'm comfortable with the situation and he keeps giving me everything he's got.
"We are delighted to have him and would I love to be able to say Johan has signed a new three-year contract? Absolutely. We haven't got to that stage yet but we will continue the dialogue."
Asked if Elmander was giving the impression he wanted to stay, Coyle added: "Yes he does, but footballers are strange characters in many ways.
"I have been there myself and sometimes when you are in a run of form you don't want too many distractions or to be talking about contracts. I can understand that.
"But the feedback I have is that he enjoys being here and if he didn't, I don't think you would see this level of performance from him. I think that speaks for itself."
A first-minute own-goal by Richard Stearman and a goal from Stuart Holden either side of Elmander's effort meant Bolton enjoyed a 3-0 lead with a little over 20 minutes remaining.
Wolves swiftly reduced the deficit through Kevin Foley and Steven Fletcher, and Coyle admitted it had been a nervy finale before his side sealed the win which takes them up to fifth in the Premier League.
"We got ourselves into a tremendous position, but you have to give Wolves credit," Coyle said. "They showed tremendous spirit and got themselves back into the game, which added a few grey hairs to myself.
"But over the piece I don't think anyone could say we weren't worthy of the three points."
Wolves manager Mick McCarthy, whose team also conceded in the opening minute in their previous game against Arsenal, was left with mixed emotions after a late rally failed to improve his side's standing in the bottom three.
Asked if he felt encouraged or distraught by the performance, McCarthy said: "A bit of both. We made it very difficult (for ourselves) and we shouldn't have to come back from three goals down, or one after 50 seconds, that is for sure.
"It's difficult then to repair it, although I thought we had plenty of chances in the first half and I thought we started the second half well.
"It's a great goal for Elmander from his point of view, but from mine it is awful. We lost the plot for a few minutes and got caught for the third, but having come back we should have got the equaliser."