Mane was one of the star performers for Jurgen Klopp’s side in his first season at Anfield, but his season was prematurely ended when he was forced to undergo knee surgery.
The Senegal international sustained the injury during the Merseyside derby win over Everton at Anfield.
The 25-year-old has been working hard through the summer and has spent considerable time at the club’s Melwood training base to ensure his recovery plan is on schedule.
Mane has already been out on the training field with an individual programme and is now on course to join up with his team-mates.
The talented forward will not be considered for the pre-season friendlies against Tranmere and Wigan next week, but could get his first run-out when the first-team squad travel to Hong Kong for the Premier League Asia Trophy.
Liverpool face Crystal Palace on July 19 and will then face either West Brom or Leicester three days later.