Sky Sports says new Gunners boss Unai Emery is ready to splash the cash in an attempt to send Arsenal back into the Champions League.
Emery, who was only appointed on Wednesday, has a tough job to do in order to rebuild the squad this summer.
And he wants to start by adding quality in the middle of the park by landing the Italian midfielder.
The talented 21-year-old has a £26million release clause in his contract.
Pellegrini played a crucial role in Roma's run to the Champions League semi-finals and made 36 appearances in all competitions.