Parling, who featured in all three of last summer's Lions Tests against Australia, starting two, has not made the Tigers' XV since injuring his shoulder on England duty last autumn.
Youngs meanwhile, who also started two Tests Down Under and featured in all three, bolsters the Tigers' front row in a match that could see Leicester seal their play-off place, should they collect maximum points.
The Tigers crashed to Harlequins in their last Premiership outing but Cockerill is demanding improvements, having called on his British & Irish Lions.
"We have still got a semi-final spot to aim for and we were a bit disappointed with how we played at Quins in the last round," said Cockerill.
"Sale Sharks have been doing well and are also potentially still looking at the top four in the table. It's going to be a tight battle for those places with just two rounds to play."