The 25-year-old has long been tipped to leave the Reebok Stadium this summer, with Arsenal boss Arsene Wenger a known admirer.
Manchester City were also heavily linked with the former Aston Villa star, although Roberto Mancini's interest does appear to have cooled.
Cahill returned to training on Monday morning, with his future no nearer being clarified.
And whilst Coyle would love the England defender to stay, he is realistic enough to know what will happen once a suitable offer is received.
"If someone comes in with the right deal for Gary and the club, he would go with our blessing," said the Trotters chief.
"He wants to play Champions League football and there has been unbelievable speculation regarding him.
"There have been elite clubs who have noted their interest. It is up to them to take that forward.
"They need to make a concrete bid so the club can look at it, otherwise there is nothing to talk about. That is the frustrating bit.
"We don't want to lose him. Until such time as we have an offer to consider, we must focus on Bolton."
Coyle insists the uncertainty surrounding Cahill is not having a negative effect on his own transfer plans.
It is clearly obvious the defender's departure would leave a massive hole in a squad that looked set for a top-10 finish last term until they suffered a dreadful hangover after the FA Cup semi-final hammering by Stoke.
However, Coyle's plans do not revolve around one man.
"I don't have two lists of targets; one if Gary goes, the other if he stays. I have one, the players I believe can take this club forward."
Coyle is not being drawn on any attempt to bring Shaun Wright-Phillips or Robbie Keane to Bolton, preferring instead to concentrate on the new recruit he had already snared.
A Darren Pratley fan from his Bolton days, Coyle monitored the Swansea midfielder throughout last term, knowing his contract was coming to an end.
Once it expired, Bolton pounced.
"Last summer, I made it public that I wanted a new contract," recalled Pratley.
"When I was on holiday, the chairman said he was in no rush to give me a contract. I was very disappointed with that.
"It dragged on throughout the season and after the final, I looked at what clubs were around and chose Bolton.
"I could have stayed in my comfort zone but I believe I am good enough to play in the Premier League."
Following the departures of Johan Elmander and Daniel Sturridge in the summer, Coyle makes no secret of the fact he needs more forwards.
He is dubious about the potential for bringing Sturridge back north, believing new Chelsea boss Andre Villas Boas might prefer to assess the England Under-21 star's talents himself.
Despite an impressive season with Porto, question marks hang over Villas Boas' ability to impose himself on an experienced Blues squad, some of whom are the same age as the 33-year-old.
Coyle already has an insight into the Portuguese. And he does not believe there will be a problem.
"Villas Boas is a tremendous addition to the Premier League," said Coyle.
"I know him well. I did my pro-licence with him and really took to him.
"He is a fantastic manager, who has achieved such a lot at such a young age.
"He has so many attributes. He will be a great fit with Chelsea.
"There is no doubt he will be a huge success."
Source: Team Talk
Source: Team Talk