The forward has been a big hit at the Saints, putting in a series of impressive performances since joining in 2014.
He finished last season as their top goal-scorer, scoring 14 goals in all competitions as the Saints secured a European placed under Ronald Koeman.
His displays have not gone unnoticed and he has been heavily linked with a transfer away from St Mary’s this summer, with several Premier League sides linked with a move.
Liverpool are one of those according to the Liverpool Echo as Reds boss Klopp is keen to add to his attacking options for next season. As far as they are concerned, the forward would command a fee of around £30million this summer.
The Echo claims the German boss has a long-standing interest in Mane, having scouted the Senegal international since his time at Red Bull Salzburg.
However, any progress on that move is unlikely to happen until Southampton name their new manager after Ronald Koeman moved to Merseyside rivals Everton.