The 21-year-old Kenyan international, who has three years left on his current deal, has recently been linked with a move to the Premier League.
"Victor has informed Celtic the contract offer fell short of his expectations," said Rob Moore. "There were a number of aspects that fell short - he turned it down.
"He is very happy with the job he is doing at the moment. He is a great professional and his commitment cannot be questioned, but it doesn't take a rocket scientist to work out that he lost great earning potential in the summer."
Wanyama moved to Celtic Park from Belgian club Beerschot AC last summer for £900,000.