Man Utd transfer news: Red Devils eye Pellegrini deal in January
The 22-year-old has been on the radar of Jose Mourinho since January, when he was also being eyed up by Chelsea.
And United could still make their move 12 months later, after a disappointing summer transfer window.
Reports from Calciomercato in Italy suggest Roma bosses have offered their man a significant pay rise in order to persuade him to stay.
The Italian has also been told to either double or remove the £26m (€30m) exit clause in his contract.
Juventus and Inter Milan are thought have joined United in the hunt for Pellegrini, but Roma are keen to keep hold of their man having already let go of central-midfielders Radja Nainggolan and Kevin Strootman earlier this window.
Mourinho’s only major signing of Fred has struggled so far at Old Trafford following his £52million move.
He has featured in each of United’s three Premier League games so far, but failed to make any real impact just yet.
Mourinho will be pleased with the form of new makeshift captain Paul Pogba however, who has netted twice from the penalty spot already this season.
But the Portuguese is believed to still be in the market for a box-to-box midfielder, with question marks remaining over the Frenchman’s future at the club following talks of a move to Barcelona.
And with competition for the Roma man hotting up, Mourinho will need to get the backing of his board fast to secure the Italian’s signature in January.
Pellegrini caught the eye of football fans with his fine form in last season’s Champions League, helping the Giallorossi to the semi-finals, before they were knocked out by Liverpool.
He came through the Roma academy, before leaving for Sassuolo in 2015 for two years.
Having impressed at the Modena club, he then returned to the Stadio Olimpico on a buy-back clause for £8.8m.
He is widely regarded as one of Italy’s best young talents, and having already picked up six caps for his country, is touted for a big future.
Mourinho has dipped into the Serie A for midfielders before, having brought Pogba back from Juventus in 2016.
He also had his sights set on Lazio’s Sergej Milinkovic-Savic, but the Rome club’s high valuation of the player put off Old Trafford bosses.
His side will be looking to bounce back from Monday’s disappointing 3-0 loss to Tottenham when they travel to Turf Moor to take on Burnley on Sunday.