Firmino's future at Al Ahli is uncertain, as he has fallen down the pecking order under Matthias Jaissle and has not started a match for the club since late October.
The 32-year-old has scored only three goals in 17 appearances for Al Ahli, and all of those goals were netted during his debut in a 3-1 victory over Al-Hazem back in August.
According to the Mirror, Gerrard is now considering a move for Firmino that would see him reunited with former Liverpool teammates Jordan Henderson and Gini Wijnaldum at Al Ettifaq.
The report adds that The Commandos are not the only side eyeing up the Brazilian, as Al-Fateh are also believed to be showing interest in a possible loan move for the forward.
Saudi clubs are restricted to registering only eight foreign players in their official squads.
Therefore, if Al Ahli decides to part ways with Firmino next month, it would open up an opportunity for them to bring in another high-profile recruit from overseas, should they choose to do so.
The Royals have a star-studded lineup of foreign players, including Riyad Mahrez, Allan Saint-Maximin, Edouard Mendy, Franck Kessie, Gabri Veiga, Merih Demiral and Roger Ibanez.