Milner rescued City in the third round of the FA Cup on Sunday, scoring two second-half goals - the winner coming in the first minute of injury time - as the Premier League giants had to come from behind to beat Championship side Sheffield Wednesday.
The former Leeds, Newcastle and Aston Villa midfielder is out of contract at the end of the season and Goal understands that Liverpool are heading the queue to sign him if he does not agree an extension at the Etihad Stadium.
Pellegrini is eager to ensure that the 29-year-old stays put, however, telling reporters: "There is no news on the contract for the moment but I hope we will find an arrangement.
"I've said already what I think about James Milner. He's a very useful player.
"I brought him on in our last game as a substitute and I think he made more chances than a lot of players, three or four clear chances.
"He always plays at 100 per cent commitment and intensity for the team so I am happy with him."