The 21-year-old Kenyan is under contract until 2015 after signing in the summer of 2011 from Belgian side Beerschot. Wanyama's agent Rob Moore told STV: "Victor has informed Celtic the contract offer fell short of his expectations.
"There were a number of aspects that fell short - he turned it down."
Wanyama's performances have seen him linked with a move to the Premier League and Celtic reportedly rejected an offer for the midfielder in the summer.
Moore added: "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 (by not moving to England)."
- Sports & Recreation