The Croatian striker ended a season-long deal from Nantes with his eighth goal for the club in the 2-1 victory against Birmingham.
Klasnic extended Bolton's lead in the 59th minute with a clinical finish following good work by Vladimir Weiss.
Kevin Davies had opened the scoring for the home side in the 33rd minute with James McFadden pulling a goal back for Birmingham after 76 minutes after having an earlier effort disallowed.
Klasnic's fitness has been called into question but the supporters obviously like him, directing their chants at Coyle after he scored to sign him up.
Coyle said: "It has been stop-start for Ivan because of injuries but when he is fit I know what he brings to the team.
"If it is possible to do something financially then we will be in there pitching. It is not as black and white as saying, come on board.
"He is a player I like, he loves being at the club. I had a chat with him last week and I think you have have seen from his performance today he wants to be here.
"If the finance was right then I want to have him. He is a good player, a lovely guy. He is a character and the boys like him.
"You can never have enough goalscorers in your club. That is an area we need to be looking to improve."
Coyle would also like to retain the services of his two other loan players, Arsenal's Jack Wilshere and Manchester City's Weiss.
"I would love to have those two back next year," said the Bolton boss. "Jack has developed from a young boy into a man. He has been outstanding for me a on a weekly basis.
"Ultimately that decision will be Arsene Wenger's. Jack is a far better player now than he was in January because of his experience in the Premier League. I know he enjoys working here."
Coyle, who arrived in January with the club in the relegation zone, was delighted to finish on a winning note.
He added: "Our performance was terrific today. It is a great ending to our short term aim which was to keep us up.
"We came in knowing it was going to be a tough ask. We were in the bottom three and had not got enough points. We felt we could galvanise the players and get them to show their qualities."
Birmingham may have endured a disappointing run-in and recorded only one win in 10 games but manager Alex McLeish believes that should not detract from their campaign as a whole.
He said: "We have been one of the lowest spenders in the league. To come from the Championship and finish ninth in the league is an amazing achievement. It feels like winning a cup.
"We have got to prove ourselves again next season. The players have been outstanding and risen to almost every challenge we have given them this year.
"Although I thought we capable of staying in the league, we have punched above our weight."
McFadden's goal came after substitute Christian Benitez saw his penalty blocked by goalkeeper Jussi Jaaskelainen.
McLeish agreed with Coyle that referee Kevin Friend called it wrong and it was a soft penalty.
"Maybe he felt he had given Bolton too many decisions and it was time to give one to Birmingham, " said the Scot.
Source: Team Talk
Source: Team Talk