The Sentinel newspaper reports that manager Michael Brown has been impressed with trialist Michael Tonge.
The 34 year-old midfielder has been on trial with Vale over the summer after being released by Stevenage.
He is therefore available on a free transfer and according to the newspaper, Brown has been impressed by his influence on and off the pitch.
It suggests that Vale will make a move to sign the veteran on a permanent deal.
Should a deal be agreed, Tonge would complement an experienced central core of Anthony Kay and Tom Pope at the club.