Cowell is said to have tasked the veteran judge with reversing the show's "disastrous" ratings crash, apparently giving him 48 hours to decide if Contostavlos, Kelly Rowland or Gary Barlow will be axed.
"Simon will do anything to turn the show around," a source told The Mirror. "It's no coincidence that as soon as the new team came in the viewers fell off. He thinks the only way to save he show is to get rid of some of the panel.
"Louis and Simon are best friends. Louis is his eyes and ears in the show, Simon's man on the ground, so he is the best-placed person to decide who gets the chop."
Cowell has told Walsh not to worry about the potential fallout of bringing back Cole, and assured the Irish manager that he would "rather scrap the whole show" than fire him.
"Louis is a businessman," the insider added. "If he thinks Cheryl will get the ratings back up he'll tell Simon to give Tulisa the chop, no matter how good friends they are.
"Cheryl was loved by the public in a way no other judge ever has been, before or since. Her comeback would guarantee a massive ratings boost."
A spokesperson for Roland dismissed suggestions that she has decided to quit The X Factor over her feud with Contostavlos.