Mancini says he is back in his native country "to sort out family problems".
But reports and sources in Italy suggest that Mancini is being lined up to replace Fiorentina's Turkish coach Fatih Terim.
Terim joined Fiorentina after steering Galatasaray to last season's Uefa Cup final triumph over Arsenal.
But there are reports he will not be renewing his one-year contract.
It means Mancini could have already played his last game for Leicester.
He is due to hold talks next week with Foxes manager Peter Taylor.
A Leicester spokesman confirmed: "Roberto has kept us fully informed of his situation and is staying in Italy for some extra time. We plan to talk to him early next week."
Mancini added: "I am in Italy to try and sort out family problems. I hope I can and I look forward to playing for Leicester again."
Mancini has made four starts for Leicester but was only on the bench for last Saturday's 2-1 defeat at Everton.
He signed a contract at Filbert Street until the end of the season after leaving his job as head coach at Lazio folowing the departure of Sven Goran Eriksson.