Barton has been without a club since leaving Burnley following an FA ban for breaching betting rules in April 2017. His suspension will be up in June.
Nolan said of the possibility: “Me and Joey are good friends. He is a top player, a top lad and I really get on well with him.
“We will always be in touch so let's see what happens.
“Joey is probably going to want to play at a higher level. And if that doesn't come to fruition then I am sure there will be a conversation in the summer.
“He describes himself as Joey on the pitch and Joseph off it and I respect both of them very highly."