Sadio Mane was taken to hospital for assessment after injuring his shoulder in training on Wednesday, according to Sky sources.
Liverpool's £30m summer signing was hurt in a collision and left Melwood to undergo scans, although it is understood he suffered a muscle injury rather than a dislocation.
Mane is now a doubt for Saturday's game against Burnley and will be monitored as the week goes on.
The new arrival made an instant impact on his Reds debut at the weekend, scoring a solo goal as his new side began the Premier League season with a 4-3 win at Arsenal.
Mane jumped on Jurgen Klopp's back in a celebration the manager later admitted was premature.
Liverpool led 4-1 at the time but conceded twice in quick succession to let Arsenal back into the game before holding on for three points.
Klopp's side are away from home for a second straight game this weekend - at Turf Moor on Saturday - as the redevelopment of Anfield's Main Stand is completed.