The Reds lost their fourth successive defeat on Sunday after Crystal Palace came from a goal behind to beat Liverpool 3-1 at Selhurst Park.
It could happen before Christmas. Whether or not it is going to happen I do not know
Liverpool face a must-win Champions League clash at Ludogorets on Wednesday night as the Reds look to end a three-game losing run in Europe.
And former Liverpool goalkeeper Grobbelaar reckons Rodgers needs to reverse the club’s ailing fortunes in the coming games to save his job.
“I think he will have another three weeks. If he doesn’t do anything in another three weeks then I think the American’s could do something about it,” Grobbelaar told BBC Sport.
“It could happen before Christmas. Whether or not it is going to happen I do not know. But I hope that he does get it right.”
Liverpool and Ludogorets both sit joint-bottom of Group B with three points each and need a victory to retain realistic hope of overtaking second-placed Basel.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news