The Italian has been linked to dozens of vacancies since being given the shove by Inter Milan in May 2008.
But Mancini had refused to settle his £5.5million a year contract with the Italians - until now.
Available: Former Inter boss Mancini
Up against it: Benitez
The 44-year-old has been linked with Benitez's job at Anfield, as well as Real Madrid, where Chilean Manuel Pellegrini is under huge pressure despite leading the club to within a point of the top of La Liga.
And Mancini has chosen now to put himself on the job market.
The former Leicester City player had been receiving full pay for doing nothing thanks to an Inter contract that ran till 2012. But he has accepted a pay-off of between £7m and £10m to tear it up.
Reports in Italy put Mancini as a frontrunner for the Madrid job, but sources in Spain say this is wide of the mark.
Benitez, who watched his Liverpool side lose 3-1 at Fulham at the weekend, has emerged in polls as the fans' favourite, but Madrid president Florentino Perez insists Pellegrini will be given time.
'There have appeared the names of great coaches in the papers, but we are happy with Pellegrini and we are sure that he will finish the season positively,' said Perez, who in his previous reign as president of Madrid employed six different coaches in a chaotic three-year period.
Dumped: Bobby Zamora was on target as Fulham beat Liverpool on Saturday
'Real Madrid respect the press and everything that they say, but it is the club who decide and we are happy how we are.
'There needs to be patience. Real Madrid will have a wonderful season.'
Madrid are second in the Spanish League after beating Getafe 2-0 on Saturday, while leaders Barcelona only drew 1-1 at Osasuna.
But Pellegrini would be back under intense pressure again if his side lose at AC Milan in the Champions League on Tuesday.
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