Coyle is keen to keep hold of Cahill and Elmander because they turn up for training with a smile on their face.
Chairman Phil Gartside set alarm bells ringing among the supporters when he indicated the duo might have to move on as the club's debt has risen to £93million.
Former Aston Villa defender Cahill is being coveted by a number of clubs while in-form striker Elmander is out of contract in the summer.
Coyle claims he is under no pressure to sell the players and received a boost when Cahill re-iterated it was "a real joy" to play for Bolton.
Coyle said: "I am well aware that Gary is happy. You only have to see how he is playing.
"Alongside Johan Elmander, Kevin Davies and Jussi (Jaaskelainen), these are the type of players I want at this football club.
"They all all look to be happy in their work, which I what I am after. If that is the case I can get the best from them.
"The conversations I have had with the chairman and the owner (Eddie Davies) I am not under any duress to sell players. If that was the case we would have done that back in August.
"If and when the right offer comes in for anybody you would have to look at it because of the business side of football. But I do not feel under any more pressure today than I was two days ago to sell any players.
"Of course I would like Gary and Johan to stay as I am here to to try and build a team and take it on."
Cahill is concentrating on helping the club progress.
"I'm contracted to Bolton Wanderers and I'm enjoying my football and my time here," he told the Bolton News.
"The whole reason why I left Villa was because I needed to play games and the only way I was going to improve was by playing.
"I just need to keep my head down and keep focused on the job I've got to do at Bolton. It's a real joy to be part of the team at the moment."
Gartside would also like to trim the wage bill and Coyle accepts that may happen in the summer when nine players are out of contract.
"It is something I am conscious of as I inherited most of the squad, " he said. "If it helps us financially it is something we might have to do.
"Players out of contract every year at every club and we are no different. That is something we will look at at the right time, give the right scrutiny to and decide where we go from there."
Bolton face Wolves at Molineux on Saturday and Coyle expects a tough shift even though the home side are struggling to win games.
Coyle added: "Their performance levels have been very high. You saw that the other night against Arsenal and Manchester United at the weekend. Mick McCarthy is doing a fantastic job."