Firmino is looking to quit Al Ahli after just six months at the club.
Sheffield United also showed an interest in the Brazilian before Paul Heckingbottom was fired as manager.
The Brazilian star completed his move to the Saudi Arabian side following an eight-year stay with Liverpool.
In that time, Firmino made 362 appearances for the Reds, scoring 111 times in the process.
He also contributed to Liverpool's bulging trophy cabinet, helping them to win the Premier League, Champions League, FA Cup, EFL Cup, UEFA Super Cup and Club World Cup in that time.
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Fulham are looking for an experienced striker to lead their line after losing talisman Aleksandar Mitrovic to Al Hilal over the summer.
Joining Al Ahli over the summer, Firmino got off to a perfect start by being named captain and scoring a hat-trick in his first match against Al-Hazem.
However the Brazilian star has failed to score since, being limited to just three goals in 19 appearances in total.
Firmino has also endured an awful time off the pitch, with his father tragically passing away of a heart attack during a family holiday in mid-November.
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A modern-day Premier League legend, fans will be very happy to see Firmino and his trademark smile strutting his stuff in English football once again.