The burly frontman has struggled to live up to expectations in England since completing a big-money move from Toulouse in 2008.
A lack of goals has severely damaged his confidence and seen him become an easy target for disgruntled supporters.
Coyle, though, has been impressed by what he has seen from Elmander during his short time in the Bolton hot-seat and insists the 28-year-old remains an integral part of his first-team plans.
"Yes, Elmander is a player I want to keep, his attitude is brilliant," Coyle told Aftonbladet.
"I have told him that anyone who plays up front in my teams must be ready to work their socks off, and Elmander has worked hard every day in training. He has been brilliant.
"He came to Bolton with a very good reputation and I can see why. He has all the weapons a really good player needs.
"I am going to give him a chance and it will be up to him to take it."