The 29-year-old England midfielder has been embroiled in protracted talks over a new long-term contract, with his current deal set to expire in the summer.
Liverpool, Arsenal and Serie A club Roma are reported to be interested in the former Newcastle and Aston Villa player and Pellegrini has suggested any dispute is not about money.
“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,” he said.
“You must ask James what is happening with him. I hope he will find an arrangement, and I think it’s possible.”
Milner, who has 53 international caps, signed for Manchester City for ??26million in 2010 and has made 186 appearances for the club, scoring 16 goals.
He began his career at hometown club Leeds United before moving to Newcastle for ??3.6m in 2004 and then Villa for ??12m in 2008.