The Scottish champions had accepted a bid, thought to be in the region of £12million, though the south coast club were unable to agree personal terms with the midfielder.
The 21 year old has welcomed offers from other parties now his current club have made it clear they are willing to sell.
Newly promoted Cardiff City are expected to make an offer, while fellow Premier League clubs Stoke City and Liverpool are also keeping an eye on events as they unfold.
Wanyama put himself in the spotlight after a number of highly rated performances in last season’s Champions League when Celtic reached the last sixteen of the competition.
He has made fifty-five league appearances for the Neil Lennon’s side, scoring ten goals, and was recently named the Clydesdale Bank Premier League Young Player of the Year.