Leicester Tigers and England international Ben Youngs could miss the November Test series.
Youngs has had surgery on a shoulder injury sustained against South Africa and is now expected to miss the opening months of the season.
"Ben has had surgery and he is having holiday time at the minute, which is important," Cockerill told the Leicester Mercury.
"He will miss the first rounds of the Heineken Cup (October 12/13/14 and October 19/20/21), which is not ideal because you want your best players playing in the biggest games."
Leicester's Micky Young and Sam Harrison will be expected to cover for Youngs throughout his absence.
England face Fiji, Australia, South Africa and New Zealand in the November Tests.
