Sampdoria are 18th in the 20-team table with nine points and lost 2-1 at Fiorentina on Sunday.
Rossi has had an eventful last four years. He was in charge of Palermo from 2009 until February 2011 when he was sacked, then reinstated three weeks later and stayed until the end of the season.
He was in charge of Fiorentina for most of the 2011-12 season, but was fired after attacking Adem Ljajic, his own player, after the Serb complained at being substituted. He took over at Sampdoria in December.
Five coaches have lost their jobs this season. In other changes, Cagliari replaced Ivo Pulga with Diego Lopez before the season started, Catania replaced Rolando Maran with Luigi De Canio in October and Genoa fired Fabio Liverani after seven matches.
Italian media also said that Milan president Silvio Berlusconi had still not decided whether to stand by his beleaguered coach Allegri and was pondering possible replacements.
Milan have taken only 13 points from 12 games after have failed to win in their last six in all competitions.
- Sports & Recreation
- Adem Ljajic