The Scottish Sun says Hoops last night agreed a record-breaking £10million-plus fee with Southampton for Wanyama.
Celtic have officially granted Wanyama, 21, permission to talk to the Premier League side.
Wanyama admitted last night that he is weighing up a megabucks move — with just personal terms to be thrashed out.
The huge Wanyama fee will shatter the Scottish record of £9.5m Spartak Moscow paid Celtic for Aiden McGeady in 2010.
It will also represent a massive profit on a young player signed from Belgian minnows Beerschot for just £900,000 two years ago.