Pellegrini has started the new season with six goals in eight appearances in all competitions for Jose Mourinho's side.
According to Calciomercato, the Italian international is now close to agreeing a new contract with Roma, ending Real Madrid's chances of signing him on a free transfer.
The report adds that talks were held yesterday and that an announcement is expected in the coming days.
The new deal would see Pellegrini stay in Rome until 2026 and earn €4m (£3.46m) a year, becoming the second-highest paid player at the club behind Tammy Abraham. His €30m (£26m) release clause would also be removed. body check tags ::