The Reds were thought to be in advanced negotiations over the German World Cup winner until he snubbed a move to Anfield earlier this week in favour of staying at the Allianz Arena.
As a result, numerous reports now suggest that Liverpool have joined the race to sign Mane, although Southampton are unwilling to sell the Senegal international for less than £25m.
Fierce rivals Manchester United have been heavily linked with a move for the attacker in recent transfer windows, while former Saints boss Mauricio Pochettino is also thought to be interested in teaming up with him at Tottenham Hotspur.
However, Jurgen Klopp is hopeful that his link with Ralf Rangnick - the former sporting director for Red Bull Salzburg while Mane was at the Austrian outfit - could help his cause should the move for Gotze completely fall through.
Mane registered nine assists and scored 15 goals, including four against Liverpool, during the 2015-16 campaign.