The 28-year-old made his first Aviva Premiership start of the season on Saturday during the Tigers' 20-11 win over London Irish before he was forced off with a hamstring problem.
"We hope in the next couple of weeks he will be fit to play," BBC Sport quotes Cockerill as saying.
"It's probably not quite as bad as we first thought, the hamstring strain is a mild one. That, at least, is some good news."
Leicester continue their league campaign on Friday night when they travel to Gloucester Rugby.