Liverpool boss Brendan Rodgers goes into the derby against Everton with his job on the line.
Boston-based Fenway Sports Group who own the Reds have shown no appetite to sack Rodgers, who ended last season with a 6-1 hammering at Stoke and has had an erratic start to the new campaign.
But the People says Anfield sources have suggested a demoralising defeat in the 225th Mersey derby at Goodison Park on Sunday will shift FSG's thinking.
Former Real Madrid and Chelsea boss Carlo Ancelotti and former Borussia Dortmund chief Jurgen Klopp head a list of available managers who would jump at the Kop job if FSG do dump Rodgers.
Senior Liverpool figures believe the 12-day international break to be a key window of opportunity for FSG if Rodgers and his stars suffer defeat against their neighbours.