Fowler was linked with a swift return to England to link up with former team-mate John Barnes at Tranmere even before he had taken part in a Fury training session, while the latest rumours link the 34-year-old to clubs in Asia, the Middle East and Europe.
"I've no doubt we'll get requests but to those guys, I would stop them and say, 'don't waste your time'," Matheson told The Australian newspaper.
"Everyone has their price but at the moment I have got a massive, massive value on building this club and you can't buy what Robbie is providing us at the moment.
"The camaraderie he brings in that side and that passion in there he shows for his captaincy and the form he's in, you just can't buy that."
Fowler's fourth A-League goal in six games, a brilliant dipping strike from outside the area, earned North Queensland a first ever A-League win and is an early contender for goal of the season.
And after Jade North, Brendon Santalab and Felipe all departed for foreign shores this year, Matheson is ready to turn down more substantial offers for Fury captain Fowler, who has signed a two-year contract at Dairy Farmers Stadium.
"It wasn't money that brought Robbie here, it was the lifestyle," added Matheson.
"Clubs have already offered him significantly more than what we could - it was lifestyle that got him here - and why would I let go probably the best thing we'll ever own?
"The way he's playing the game and the ease he is scoring some of these goals is telling us he hasn't lost his touch and that would clearly be an asset to anyone's club.
"Big, cashed-up clubs would want to capitalise on that and there is no doubt that in the coming weeks and months we'll be approached and I can say money can't buy that."