The stopper was a member of England’s World Cup squad after breaking into Roy Hodgson’s squad on the back of some excellent displays for the Bhoys.
He has long been linked with a move south of the border, and the Saints are set to win the race in the coming weeks.
Celtic are resigned to letting the 26-year-old leave, but they want him to stay in Glasgow until at least the end of the week with the club set to play the second leg of their Champions League qualifier Legia Warsaw on Wednesday.
The Scots trail their Polish counterparts 4-1 and their likely exit will leave them unable to keep Forster.
Craig Gordon has been signed, and the former Sunderland man could be used as a replacement.
Forster is valued at around £8m, but any fee to be paid is as of yet unknown.
The ‘keeper’s arrival will give Southampton the green light to offload Artur Boruc, who is wanted by a host of clubs.
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