Kearns made 12 appearances during a loan spell at Bootham Crescent earlier this season but has not featured for Posh since returning to London Road.
"He's available again, although I've heard he might be going to Rotherham," Mills told The York Press.
"The problem we have is with the money side of things, whether that's a transfer fee or to do with his salary. "It's unfortunate that we can't compete with the likes of Rotherham in that respect, because he did well for us and he would be an option out wide for me at the moment.
"We all know the qualities he has got and you never know what might happen.
"It could come down to whether we can make Peterborough an acceptable offer but I don't know whether we are in a position to do that."