The Scottish Sun says the Kenyan midfielder rejected the Hoops' most recent offer, with clubs in England and abroad lurking.
Hoops boss Neil Lennon is bracing himself for a big money offer for Wanyama with several clubs, including Manchester United, keeping tabs on his situation.
He said: "I would not be surprised if we get an offer, but I'd be surprised if we accepted it.
"Victor is happy and enjoying his football, but you can't stop progression. If a bigger and more productive club come in and the offer is right, we will seriously look at it.
"I don't want to stop their progress. I will shake his hand and say 'Good luck to you, son' - so long as we get about £25million!"