The 25-year-old forward -- who shone for Liverpool last season scoring 13 goals after joining from Southampton -- suffered the knee injury in the derby with Everton on April 1.
His absence at the Africa Cup of Nations earlier in the year had already proved costly to Liverpool's title ambitions. Due to the injury Mane missed eight games at the end of the campaign, but Liverpool still secured a crucial Champions League spot.
A statement from the club on Thursday said Mane "is on schedule", adding he is on course to join training "within a time frame of 10 days".
"He will continue to be monitored and assessed by the club's medical staff to ensure he returns in the best shape and ready for the remainder of the pre-season schedule."