No matter the result in Sunday's FA Cup fourth round tie with Aston Villa, Levy won't act on Postecoglou's position, says The Sun.
Even a heavy defeat won't shake Levy, who remains behind the Australian.
However, with league games against Manchester United and Ipswich Town up next, Postecoglou has hinted the coming two weeks could be decisive regarding his future.
He said, “There’s a number of our players scheduled to come back during that time, so we’ll use it wisely to rest the guys who need rest.
“Certainly, there’s a fair few that need some rest and also hopefully get some work into the guys who have been out for quite a while to be ready for the challenge ahead.
“Because I think these two weeks we’ve got now will be really valuable for the finish of our season.”