Elmander, whose contract expires in the summer, has caught the eye this season and will be looking to improve his eight-goal tally against Blackburn on Sunday.
The club are in talks with his agent but the Swede has indicated he will wait until the end of the season before deciding on his future.
That has given Coyle hope of keeping the player at the Reebok Stadium.
He said: "I know Johan is happy. That goes without saying. You can see it in his performances. He would not be performing like he is and playing well if he was not content.
"He came with a big price tag and reputation but he has always applied himself in terms of his work-rate. The longer he is here the better chance I have of retaining him for a further period. We will continue the dialogue."
Source: PA
Source: PA