Davies is looking for a new club after his ten-year stint with Bolton came to an end earlier in the summer, and he has been linked with teams such as Sheffield Wednesday, Blackpool, Burnley and Millwall.
Preston are also interested in the free agent and Grayson admits he will have to remain patient as he tries to get his squad sorted for the start of the new season.
"We're still waiting to see where Kevin Davies is at," Grayson told the Lancashire Evening Post:
"It will come to a point where he has to make a decision, and we do as well.
"He has to get back into training and we want to know where we roughly are with the squad.
"I think Kevin has found it a little more difficult coming round to the fact that he is an unemployed footballer, as such.
"He has got a few options and has to consider which is the best one for the next year or so of his footballing career.
"We are certainly still in with a great shout of getting him, although there are other teams involved too.
"We hope to have ticked enough boxes for him to come here. If he doesn't come here we will move on to our next target because we have a few more options available to us.
"I'm in contact with Kevin every other day, finding out what is happening. He has been good enough to let us know what his thoughts are."
There could also be a couple of players leaving Deepdale this summer, with Grayson ready to listen to offers for high-earner Iain Hume after he spent last season on loan at Doncaster Rovers.
Chris Beardsley has also been linked with a move elsewhere, although Grayson insists he would be happy to keep both men if transfers do not materialise.
He said: "With Chris we are just waiting for someone to make an offer to take him. As for Iain, it is pretty much wait and see.
"People are saying X, Y and Z about what is happening with Doncaster and Iain. We'll see if there is an opportunity to move him on and if no offers come in, he is a contracted player who will available for selection.
"Neither player has been discarded - they have been training on a daily basis, showing their enthusiasm and a fantastic attitude."