The 21-year-old has been heavily linked with a switch to the Saints after the SPL champions were reported to have accepted a £12m bid from the south coast club.
Wanyama was previously linked with a move to the Red Devils, and the Kenyan’s agent Ivan Modia insisted the midfielder is no longer in talks with Southampton.
“We are not in talks with Southampton and have not been since their final offer of terms, which was more than two weeks ago,” Modia told Sky Sports.
“The news of the fee being agreed may just be coming out now, but we see little sense in a fee being agreed if there is no reasonable prospect of the player’s terms being met.
“To suggest we are talking with Southampton is totally false, their offer was way below Victor’s expectations. There is no chance of him signing the deal on offer and, in fact, both Celtic and Southampton were informed of this some time ago.
“The player will not be forced into a corner to accept the Southampton deal, just because it is good for Celtic. Remember, he has been with the club for two years now – without a pay rise – and has given them wonderful service ever since he arrived.
“Added to this is the fact that by Celtic refusing him permission to join Queens Park Rangers last summer, Victor lost more than £1million in potential salary earnings – yet he just kept his mouth shut and continued to be a model professional. Many other players may not have adopted this attitude, in the circumstances.”
Wanyama has scored 13 goals in 91 appearances for Celtic after joining the SPL champions from Berrschot AC in 2011.