The BBC reports that the ex-Newcastle goalkeeper will return to the club provided he passes a medical.
The 31-year-old has fallen down the pecking order at St Mary's, and is effectively third-choice behind Angus Gunn and Alex McCarthy.
Celtic sold the 'keeper to the Saints for £10 million five years ago, and the England international has since made 125 appearances for the English Premier League side.
Neil Lennon has been looking for reinforcements between the sticks following injury to No.1 Scott Bain.
The former Dundee goalkeeper suffered a dislocated thumb last week, with back-up goalie Craig Gordon given the nod for the Betfred Cup match against Dunfermline last weekend.
If the move goes through, Forster - who won three league titles with Celtic and made close to 200 appearances during his first spell - could compete with Bain and Gordon for the gloves.