The 32-year-old Brazilian is reportedly ready to leave Saudi Arabia after just half a season in the Pro League.
Firmino became one of the most high-profile stars to move to Saudi Arabia for big money last summer. He joined Al-Ahli after his eight-year stay at Liverpool came to an end following the expiry of his contract.
However, the former Hoffenheim star's stay in the Middle East has not gone to plan.
After scoring a hat-trick on his Saudi Pro League debut, the Brazilian hasn't netted since and has struggled for game time in recent months – last starting a game in October.
Recent reports have claimed that the forward – who also tragically lost his father in November – has 'lost patience' in Saudi Arabia and is seeking a return to either Europe or Brazil.
Sheffield United were one team recently linked with the man who scored 111 goals for Liverpool, while talkSPORT now claim that Fulham are 'among the Premier League clubs who have been offered the chance' to take on Firmino.
The report claims that Fulham are looking for an experienced striker to add to their squad, following the exit of Aleksandar Mitrovic (also to Saudi Arabia) last summer.
Marco Silva's side sit in 13th in the Premier League table after 20 games, while 32-year-old Raul Jimenez is their current top scorer with five goals.
Firmino was in the crowd at Anfield for the Reds' 4-2 win over Newcastle on New Year's Day, and told the club's official website of his 'emotional' return.
"I'm very happy to be back here at home, at Liverpool and the stadium as well, Anfield. I'm very grateful to God for bringing me these moments again, to watch the game. Of course I'm not playing but I watch the game and see the boys," he said.
"It's always emotional [to be here], you cannot forget you were here. We had a very good history here at the club that we achieved together and nobody can claim this history, it's already in the history [books]. We are here to support."