The midfielder is already wanted by several clubs in Italy after catching the eye with his performances in Serie A this season.
Juventus and Inter Milan are tracking the 20-year-old, while Roma - who sold Pellegrini to Sassuolo for £1m in 2015 - can buy him back if they fork over £8.5m.
But the Italian clubs look as though they will face competition from England as, according to Corriere dello Sport, Chelsea and Manchester City are scouting Pellegrini.
The Italy under-21 international is said to have attracted the attention of the Premier League pair and they are now stepping up their efforts ahead of the summer transfer window.