The Liverpool star is one of the best attackers in the world and finished the 2019/20 season with 20 goals in all competitions.
Zinedine Zidane is thought to be a big fan of Mane and was linked with a move for the Senegal international, although a deal never materialised.
Recent reports in Spain claim Mane might be open to a switch to Barcelona with his former Southampton manager Ronald Koeman now in charge at the club.
Spanish outlet Sport play down the possibility of Mane joining Koeman at Barcelona this summer, but do claim the forward was left ‘very angry’ with Liverpool’s refusal to speak to Real Madrid last year over a deal.
Liverpool are not expected to make any major signings this summer or permit the exit of one of their main performers.
Mane and his team-mates are still basking in the glory of the club’s first ever Premier League title triumph, even with the new season right around the corner.
The Reds begin the new campaign at home to newly promoted side Leeds United, but play Arsenal in the Community Shield on Saturday.
Klopp was quizzed about his side’s lack of transfer activity, with left-back Kostas Tsimikas the only signing the Reds have made this summer.
‘We bought players in already! Kostas, the kids are getting closer,’ Klopp said ahead of the game against Arsenal.
‘Numbers in the squad make sense, we have a big squad at the moment with a lot of young boys.
‘The size of the squad is okay at the moment. I’m happy with what we have but we look constantly for improvement – internally too.’