The 27-year-old - a 2016 arrival from Southampton - only penned an improved deal with the Reds last November, which runs until June 2023.
However, according to La Gazzetta dello Sport journalist Nicolo Schira, the Champions League winners have opened fresh talks with the Senegal international over a new contract worth £220,000 a week.
The wages reportedly on offer would place Mane as the club's highest earner above Mohamed Salah, who earns slightly more than the likes of Roberto Firmino, Virgil van Dijk in terms of basic weekly wage.
Schira claims that Liverpool are keen for Mane to sign until the end of the 2024-25 campaign as they look to secure the future of a player who has been in excellent form over the last 12 months.
The Senegalese scored 26 times in 50 appearances for Jurgen Klopp's side during the 2018-19 campaign, while he has managed six goals in seven outings at the start of the new campaign. body check tags ::