The Brazilian sustained a hamstring injury in Liverpool’s 2-1 win over Aston Villa on Tuesday, prompting fears his season was over, but Klopp thinks he could win his race against time to play in Paris on 28 May.
“There’s a good chance that he will be available for the Champions League final,” the Liverpool manager said.
In the meantime, captain Jordan Henderson is set to take Fabinho’s position as Liverpool’s defensive midfielder against Chelsea at Wembley on Saturday, with Klopp insisting they have to find a way to get by in his absence.
“We have to,” he said. “Because we can cope. Having him or not having him is a difference but it is all fine. That’s normal stuff that happens. It’s never in a position where you have 12 options, it’s always in a position where you [don’t].
“We have a few players. Hendo came on and played incredible, he has played super games this season at 6 so that is not a problem.”
After the FA Cup final, Liverpool finish their Premier League campaign away at Southampton and at home to Wolves.
Chelsea face their own injury issues in midfield at the weekend after Thomas Tuchel confirmed Mateo Kovacic will miss the final, following a red-card challenge by Dan James in the Blues’ midweek win over Leeds.
Liverpool beat Chelsea on penalties in the League Cup final at Wembley earlier this season, while both Premier League matches between the clubs this term ended in draws.