The 26-year-old England international has already travelled to St Mary's, where he is expected to sign a four-year deal.
Forster has been long linked with a switch to the south coast, with the Scottish club having rejected what they described as a 'derisory' bid for the goalkeeper earlier in the window.
It was thought Celtic’s Champions League reprieve would have made a swoop for the highly-rated stopper, who has enjoyed impressive form in Europe over the past few seasons, even more unlikely for the Saints.
But it seems the Bhoys have instead allowed the star to leave, with rumours suggesting they have accepted an improved offer in the region of £10million from Southampton.
Forster is already in the south coast for a medical, with Southampton hoping to finalise the deal over the weekend.
