The 25-year-old midfielder has a year left on his contract with Roma and it also contains a release clause worth €25m.
The Italian’s contract situation means that several clubs are interested in getting their hands on him in the ongoing transfer window.
Liverpool are believed to be interested in the midfielder and are considering taking him to Anfield this summer following the departure of Georginio Wijnaldum.
But Roma are keen to hold on to him and, according to Italian daily Corriere dello Sport, they have prioritised offering the midfielder a new contract.
The 25-year-old is the club captain at Roma and Jose Mourinho is said to be been on retaining him as well.
Roma have paused contract talks with other players, but Pellegrini is the exception and they are prioritising discussions.
They are looking to convince Pellegrini to sign a new five-year contract and stay at Roma.