Leicester have won four of five Premiership games since the competition recommenced after a two-month break for the Six Nations.
It was at the start of the league hiatus that the hugely experienced Cheika – who previously guided NSW Waratahs to Super Rugby success and Leinster to European glory in the Heineken Cup in 2009 – confirmed he would not stay beyond his one-year contract with Tigers.
In Parling they will have a rookie head coach.
He has had two spells working with the Australian national team since 2020, having first moved into coaching with Melbourne Rebels where he retired as a player in 2018.
Cheika says the Tigers job will be a “huge opportunity” for the the former England lock, who also featured for the British and Irish Lions in 2013.
In announcing the appointment of Parling, who will be the ninth head coach to lead Leicester in nine years, Tigers repeatedly said he takes the helm on a long-term deal.
When asked about how important it would be for Tigers to find stability in the role, Cheika replied: “I think yes, I suppose. But who knows?”
The Australian continued by saying he feels he has a part to play in ensuring there are foundations to build on.
“I get all that, the stability and all that business,” he said.
“But if you just focus on what you are doing now, then that will happen by nature. I can do that by trying to bring my best quality to training every day and help start that stability by being well prepared for training and having good quality training.
“If I can help try to create that consistency on a day-to-day basis now, I have no doubt the playing roster that is here now will continue that into the future.”