The publication understands the Premier League titans will travel to Glasgow after agents for the £10m (Sh1.374b) -rated Kenyan international snubbed an improved, extended contract offer from the Parkhead club.
Wanyama’s agent Ivan Modia, who represents the player along with South African-based business partner Rob Moore, told Sportsmail: “We had a meeting with Celtic in the first week of October and the proposal was rejected shortly after the meeting.
“We have not held further discussions and it is up to Celtic if they want to resume talks with a different proposal.”
At the request of manager Neil Lennon, the Scottish champions entered discussions with a raft of their key Champions League performers, tying down James Forrest, Charlie Mulgrew and Adam Matthews on new deals.
However, talks with Wanyama and star striker Gary Hooper have not been settled.
Liverpool watched Hooper in Tuesday’s 2-1 defeat in the Nou Camp, with contract talks ongoing.
But it is Wanyama who is attracting the biggest interest, despite Celtic offering no encouragement to Queens Park Rangers in the final hours of the last window.
The SPL champions want Sh1.374b and won’t sell for less.
“It’s not a problem for Victor. He is very happy at Celtic and is grateful for the opportunity the club has given him,” added Modia.
“He has loved every minute of his time here and will continue to be the consummate professional. He will continue to give his all for the club.
“He still has two years to run on his contract after this season so there is no urgency to agree new terms.
“’We are aware of interest but he is contracted to Celtic. It is up to them to determine what happens.”
Wanyama’s current deal with the Scottish champions lasts until 2015, but Celtic were keen to tie him to a new contract to fend off interest from several English Premier League clubs including Manchester United.
However, the 21-year-old, who joined Celtic from Belgian side Beerschot in 2011, doesn’t believe the Hoops’ offer reflects his value and he has rejected the deal.
Wanyama’s agent Rob Moore told STV on Thursday adds AFP: “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.”
Celtic reportedly turned down an offer for Wanyama from an unnamed club in the close-season and, while Moore insists his client remains happy at Parkhead, he believes the Nairobi-born star deserved to be rewarded with a significantly improved contract for staying committed to Neil Lennon’s team.
“He is very happy with the job he is doing at the moment. He is a great professional and his commitment cannot be questioned,” Moore added.
“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).”