The Daily Star says Saints will turn to Redknapp if they lose faith in current manager Nigel Adkins.
The Saints board see their former boss, sacked by Spurs in the summer, as the ideal man should they end up in a Premier League survival scrap.
Redknapp, 65 endured a torrid spell at St Mary's back in 2004-05 when he could not prevent them being relegated to the Championship.
But since leaving Southampton, his stock has risen after leading rival outfit Portsmouth to FA Cup glory and Spurs to a fourth-placed Premier League finish twice in three seasons, as well as into the last eight of the Champions League in 2011.
West Ham United, another of Redknapp's old clubs, have been heavily linked with a move for him in recent days and it is the same with QPR.