Both players are due to see their current deals expire in the summer of 2023, as is their fellow striker Mohamed Salah.
Much of the focus on renewals has surrounded Salah, who is reportedly refusing to budge on his wage demands, but Firmino and Mane could also leave the club in 18 months' time.
The Athletic claims that Liverpool have not yet decided whether or not they will offer the duo extended deals, while the players themselves could reject any offers if they do arrive.
Both players will be 31 by the time their current contracts come to an end, and Liverpool have been increasingly linked with younger attackers as alternatives to their long-standing front three.
Barcelona have been credited with an interest in Firmino should Liverpool decide to cash in on the Brazilian before the end of his contract, although there is no chance of a deal being struck in January.
Between them, Firmino and Mane have made 553 appearances for Liverpool, scoring 201 goals and assisting a further 116.