McGeady joined North End on loan in August and has contributed four goals and eight assists in the Championship.
The 30-year-old winger has one year remaining on his contract with Everton, but Grayson has made it clear he would like to keep McGeady in the long-term.
"We'd like to [keep him], and I think Aiden has made it clear he would like to stay," he told BBC Radio Lancashire.
"The problem is that he has a year left at Everton. But we'll do as much as we can to make sure he's a Preston North End player next year.
"Do we go and sign him on a long-term contract, or do we try to get him on another season-long loan? Negotiations will happen with Everton because we would be foolish not to ask the question.
"It is something that will take care of itself, probably at the back-end of the season, but it's something that we would like and I'm sure the supporters would too, because he's been exceptional for us."
Republic of Ireland international McGeady began his career at Celtic and played for Spartak Moscow before joining Everton in 2014.
He spent four months of the 2015-16 season on loan at Sheffield Wednesday and has found form at Deepdale this season, featuring in each of Preston's last 13 Championship games as they picked up 21 points from a possible 39 and move up to eighth place.
Preston manager Simon Grayson believes the club would be "foolish" not to try and sign Everton's Aiden McGeady.