The Finn is coming off contract and a target for West Ham United.
"I want to make it clear that I want him to stay," Coyle told the Bolton News.
"I had a very good chat with him last week and he knows my feelings on the matter.
"We know we have Adam, and that would give us two top keepers, but we want that strength in depth. We know how good a goalkeeper Jussi is, the fantastic service he's put in for Bolton over a number of years, and we have put an offer to him that we think is a good one.
"Jussi was disappointed when he lost his spot, and he was unlucky that it happened because of an injury but he knows how far Adam has come along.
"It's up to him now whether he wants to stay and challenge him, or move on."