Jurgen Klopp has turned to the Saints winger after Mario Gotze made it clear he would prefer to stay at Bayern Munich for another season.
But The Sun claimed over the weekend that Manchester United are also keen to prise the attacker away from St Mary’s.
Both Premier League giants have cash to splash and are willing to spend £25m to bag the 24-year-old.
United tried and failed to sign Mane last summer while Tottenham were also interested in the Senegal international.
Mane cost Saints a bargain £11.8m from Red Bull Salzburg in 2014.
But Ronald Koeman wants at least double that for his influential goal scorer.
United could be in the market for a new winger with Mephis Depay's future at the club in doubt.
Jose Mourinho will be appointed boss at Old Trafford this afternoon and he might be tempted to offload the maverick Dutchman.
Mane made history last May when he scored the fastest ever Premier League hat-trick in just two minutes and 56 seconds against Aston Villa.
