Coutinho was forced off the field after just 13 minutes at Vicarage Road, after a robust challenge from Hornets centre-back Adrian Mariappa.
But according to the Telegraph, Coutinho should be passed fit to feature against the Saints on May 7.
This comes after Coutinho’s return to the Reds’ Melwood training facility, with his issue not deemed to require a scan.
A decision will be made as to whether the 24-year-old can rejoin his team-mates in training on Thursday, as Klopp plots for another three points in the top-four race.
Coutinho’s availability would be a major boost for the Reds, with just three games left to play before the end of the season.
With their 11-goal forward in tow, the Reds have an increased chance of success between now and their final game of the season on May 21.
The England duo came on as substitutes during the victory over Watford, with Lallana replacing Coutinho, and provide Klopp with a selection quandary as prepares for the Saints.
Alternatively, Sturridge’s bright cameo at Vicarage Road could prompt Klopp to hand the 27-year-old his sixth Premier League start of the season.
Even if Coutinho is only fit to take up a place on the bench, his fitness is less of an issue now than it would have been two weeks ago.
Nevertheless, Klopp will be eager to name his No. 10 from the start at Anfield, giving his side the best chance of taking all three points.