The midfielder was involved in a clash of heads in the final minutes of the Reds' 3-1 Champions League victory in Portugal on Tuesday.
He quickly returned to the field after a brief period of treatment, while Jurgen Klopp later played down the seriousness of the blow.
The German said: “It’s a cut. He’s fine. That’s how it looks.
“He had a cut in the back of his head and obviously he has no hair to hold the blood back, that’s why they needed a bit of time.
“But he should be completely fine.”
"Is there still hope? Yes, of course - but it depends on Liverpool because, as of today, Salah has no intention of accepting the opening proposal. He wants to continue, but only on his conditions." 🔴 https://t.co/iNL5SHhrj6
Despite those words of reassurance from Klopp, it was still feared that Fabinho might fall foul of concussion protocols subject to further examination.
However, it is understood that the Brazilian ultimately did not require further treatment, other than to the minor cut he sustained.
And, with the club's medical staff confident a concussion was avoided, he has been given the all clear to train ahead of this weekend's trip to the Etihad Stadium.
Barring any surprise injury setbacks, Klopp will have a full squad to choose from for Sunday's game against Pep Guardiola's side.