Milner is out of contract at the end of the 2014-15 Premier League campaign but the 29-year-old is no closer to extending his contract with City.
The England international's reluctance to recommit to the club has alerted rivals Liverpool, Arsenal and Serie A high-flyers Roma.
However, Pellegrini is not giving up hope of retaining Milner's services.
"I don't have any news about James Milner," he said.
"To decide to sign a contract you need both parties to agree it. We will see what happens from now until the end of the season.
"Maybe City have already offered all that the club can offer, maybe it's not about more money, maybe there are different things to sign a new contract.
"You must ask James what is happening with him. I hope he will find an arrangement, and I think it's possible."
Milner has scored 16 goals in 186 appearances since joining City from Aston Villa in a deal worth £26 million in 2010.
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