The Tigers centre has made just one appearance this season, in the home win over Newcastle Falcons back in September, and is working his way back to fitness after surgery on a pectoral muscle problem.
“Manu is doing well, it looks like we’ll have him back to play at the end of February, give or take a week,” said Cockerill.
“Like all of our injured players, we take the advice and if they need more time to recover fully, they get the time. We’ll want to make sure he is completely right before we bring him back.
“He is an important player and we’ve been missing key players throughout the season so far.”
Long-term injury victims Geoff Parling (shoulder) and Tom Croft (knee) are also doing well in their rehabilitation.
“Geoff is probably looking at getting back a little bit after Manu,” said Cockerill. “Crofty has had a couple of significant injuries but he’s doing very well and he will have all the time needed to make a full recovery.”
Logovi’i Mulipola is also approaching fitness after suffering a calf injury playing for Samoa during the autumn internationals.
Gonzalo Camacho remains sidelined after surgery on a shoulder injury picked up playing for Argentina before he even arrived at Welford Road.
Graham Kitchener, Mathew Tait and Niall Morris are all hoping to be fit in time for the resumption of the Aviva Premiership programme, when Tigers go to Worcester Warriors on February 7, after all three were injury victims in the match against Ulster last week.
“Kitchener had an ankle injury but should be back in a couple of weeks, same with Mat Tait who had a knock on his back,” Cockerill said.
“Niall dislocated his thumb and he may need something doing with that.
“Jordan Crane will be a couple of weeks, he landed on the point of his shoulder but it shouldn’t be too serious.
“It’s not perfect picking up more injuries, but that is the nature of the game. You play physical games like that and you will pick up bumps and bruises.”
Tigers are also monitoring the knee injury that kept Miles Benjamin out of the Ulster match.
“Miles finished the game against Treviso without a problem,” said Cockerill. “But the knee swelled up and it didn’t settle down as we would have expected so we’re investigating it a bit further.”