The Liverpool forward missed the midweek win over Watford due to the ankle injury he suffered in the previous match at Manchester United.
But Firmino will be monitored ahead of the clash with Everton with a view to being available for the Premier League-leading Reds.
“He was out there in the running yesterday but we have to see how he reacts. I will see him in a few minutes for the first time since yesterday,” said Jürgen Klopp at his pre-match press conference.
“He is very positive, that’s Bobby’s nature. We have to see. I don’t see any other player – OK, we have maybe two or three more of them – being even in contention for that game after the little problem he had.
“It looks really good but if he will be ready for Sunday, I don’t know in this second.”