Bony, who is the Swans’ record signing having joined for £12million from Vitesse Arnhem, has been heavily linked with a switch to Liverpool after an impressive debut campaign in the Premier League.
The 25-year-old netted 25 goals in all competitions last season but, despite the reported interest from Anfield, Swansea are yet to receive any bids for the Ivory Coast international
Liverpool’s pursuit may intensify after pulling out of a deal to sign QPR striker Loic Remy, but Monk insists he has no intentions of selling Bony.
"There will be interest in a number of our players - that’s the way it is - but at the end of the day, Wilf is a Swansea City player," he told the South Wales Evening Post.
"Everything that has been said about him this summer has been said in the papers. We are not a paper company, so we'll just deal with the reality.
"At the moment nobody has come in for Wilf and he is our player. But it can't drag on for the whole summer.
"We don't want one of those scenarios where it's going on right up until the last day.
"It has to be made loud and clear what is happening at some point - but at the end of the day he is not for sale unless someone comes in with an astronomical offer, which is the same with every club around the world.
"Unless anyone wants to pay an astronomical fee, he will be going nowhere."
Bony has another three years remaining on his current deal in South Wales and has previously stated that he would be happy to stay.
Monk added: "I've spoken to Wilf. He is a very good guy, a top professional, and fortunately, I get on well with him.
"Every player has ambitions and aspirations. It would be silly for any player to say 'I only want to stay at this club'.
"If a so-called bigger or better club comes along and it's a higher level, then every player is going to do it.
"That's the way it is - that's the football world. But having spoken to him, he knows he is Swansea City player and he knows nothing has happened so far.
"All he wants is to concentrate on what he is doing for Swansea City. That's why he is with the squad (in Devon). If he was thinking about going, he wouldn't be here."