The former Manchester City boss is said to be among the front-runners to replace Ranieri at Leicester City.
Former Man City boss Roberto Mancini
Ranieri was given his marching orders on Thursday evening, with the Foxes winning just one of their previous nine fixtures in all competitions.
And Mancini, who has been out of work since leaving Inter Milan last year, is said to be one of the front-runners to succeed his fellow Italian at the King Power Stadium.
Sky Sports reported on Friday that Leicester have already made contact with the former Manchester City boss, who wrote: "I am sorry for my friend #Ranieri. He will remain in the history of @LCFC, in the heart of #Leicester fans and all football lovers."
Mancini, who played for Leicester on loan during the 2000-01 season, boasts an impressive CV, having won silverware at every club he's managed.
However, should the 52-year-old take over at the King Power Stadium, his immediate focus will be on keeping the Foxes in the Premier League next season.
Former Leicester City manager Claudio Ranieri after Wednesday's loss in Seville
Last year's champions are only a point above the relegation places and are in danger of becoming the first English top flight winners to suffer an immediate relegation after his old side, Manchester City in 1937-38.
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