The speculation surrounding the attacker's future has gathered pace in recent days, with various reports claiming that Al-Nassr were closing in on an agreement for the Senegal international.
According to journalist Ben Jacobs, the two clubs in question have settled on a price, with the Saudi outfit agreeing to pay €40m (£34m) for the experienced forward.
Jacobs claims that Mane's yearly salary is expected to be around €40m (£34m), and the player has already been in touch with his new potential teammate Cristiano Ronaldo to discuss a move.
Al-Nassr had allegedly been pessimistic of their chances of signing Mane earlier this summer, but the recent activity in the Saudi Pro League, in addition to the enormous salary, has convinced the former Liverpool forward to become the latest high-profile name to agree a switch to the country.
Transfer expert Fabrizio Romano has claimed that the paperwork will now be signed before a medical examination is booked in for the 31-year-old.
Mane starred for Liverpool between 2016 and 2022, scoring 120 times in 269 appearances for the club, helping them win the Premier League, FA Cup, EFL Cup, Champions League, UEFA Super Cup and Club World Cup.
The forward left for Bayern last summer, but he found it difficult to show his best form at Allianz Arena despite managing a respectable 12 goals and six assists in 38 appearances.
Mane has another two years left to run on his deal at Allianz Arena but is allegedly being allowed to leave in order to raise the funds needed to potentially bring in Harry Kane from Tottenham Hotspur.
Bayern executives will allegedly meet with Spurs chairman Daniel Levy on Monday in the hope of coming to an agreement over a summer deal for Kane.
Mane is set to become Al-Nassr's fourth signing of the summer, following Marcelo Brozovic, Seko Fofana and Alex Telles to the club.
Ronaldo famously joined the club earlier this year, scoring 14 goals and registering two assists in 19 appearances in all competitions.
However, the Riyadh-based outfit, who are now managed by Luis Castro, only finished second in the table, five points behind the champions Al-Ittihad.
Jordan Henderson and Riyad Mahrez have become the latest high-profile players to move to the Saudi Pro League, joining the likes of Karim Benzema, N'Golo Kante, Kalidou Koulibaly, Ruben Neves, Edouard Mendy, Roberto Firmino and Sergej Milinkovic-Savic in the division.