Konate missed the 3-0 win over Brentford and subsequently pulled out of the France squad this month due to a hamstring injury.
The 24-year-old aggravated an existing problem in the warmup to Liverpool’s 3-2 defeat to Toulouse at the start of the month, needing treatment during the break.
This has been backed up by footage shared by Konate from the break, with the Frenchman working with a personal physio during time off.
Konate underwent strength and conditioning training, and was able to return to running outdoors as he steps up his rehabilitation.
That will have continued upon his return to the AXA Training Centre this week, having been among the first to report back along with the likes of Jones and goalkeeper Adrian.
“No days off,” Konate wrote on Instagram. “Big week incoming.”
Matip impressed as Liverpool kept a clean sheet against Brentford last time out, and like Konate was not on duty this month having long since retired with Cameroon.