The 29-year-old Swede has made an impressive start to the Premier League campaign with the Trotters, netting four goals in eight appearances so far.
Coyle challenged the powerful forward to earn himself a new deal and his recent hot streak looks to have done the trick.
Elmander, formerly of Feyenoord, Brondby and Toulouse, is set for contract talks in the next fortnight and Coyle is eager to get him tied down.
"I want Johan at the club and I am pretty sure we will sit down soon and talk about it," the Bolton manager said.
"He shows with his form and the things he says that he wants to be at the club."
Source: Team Talk
Source: Team Talk