Two seasons ago, the Northern Irish coach led the Reds to second place in the league table, but their form and fortunes faded last season as they slumped to sixth place in the top flight.
The Merseyside heavyweights have failed to impress so far this term, and the pressure is increasing on Rodgers after defeats to West Ham United and Manchester United, and an underwhelming 1-1 draw with Norwich City last week.
After that defeat, reports emerged that Fenway Sports Group were considering a change of leadership, and were courting Ancelotti as a replacement for the under-performing coach.
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However, according to talkSPORT, FSG are understood to have confirmed that they retain complete faith in Rodgers and are not looking for a change of leadership.
Indeed, the manager spent £80 million on new players during the summer—bringing in the likes of Roberto Firminio, Christian Benteke and Nathaniel Clyne—and to sack the coach now would appear to be something of a panic sacking.