The Sun claim the sacked Real Madrid manager is keen on returning to the Premier League.
And they suggest taking the top job at Anfield would appeal to the Italian.
Ancelotti was sacked by Madrid on Monday despite landing the Champions League last season.
The former Chelsea boss wants to take a season off to rest following his departure but could be tempted into a swift return if Liverpool decide to axe Brendan Rodgers.
The Kop boss has come under fire after a poor season.
Rodgers is not thought to be under immediate threat of the sack.
But his position may come under scrutiny if Liverpool make a shaky start next season.
