The 29-year-old, who is currently out with a hamstring injury, has been deemed surplus to requirements by Roma due to his ongoing fitness issues.
Pellegrini has been heavily linked with a move to Premier League strugglers West Ham, but that has since been rubbished by his representatives, according to Corriere dello Sport.
The midfielder is said to be keen on making a good impression on new manager Gian Piero Gasperini once he returns to fitness.
He made 34 appearances across all competitions last season, scoring three goals and providing two assists in the process.
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