The departures of Opeti Fonua to Newcastle and Jordan Crane to Bristol has weakened Tigers in the back row, but Lachlan McCaffrey and Ed Slater have both played as a number eight.
McAffrey started the first Premiership match of the season against Gloucester.
"We have got good coverage," Cockerill told BBC Radio Leicester.
"We have guys doing a very good job there but they are probably a hybrid of all three [back-row] positions.
"But we are looking for someone to potentially come into that starting slot.
"When we find the right person we will try to make that signing. If we don't find the right fit, then the lads that are there now are doing a great job and will get better the more they play.
"There is no point rushing in and getting the wrong person. The quality of the person and the dynamic of the fit with the profile of the player we want is the key part."
Leicester Tigers are still seeking to sign a first-choice number eight, but director of rugby Richard Cockerill says there is no need to rush.