Thompson has been working as a pundit for Sky Sports, but is one of four ex-Reds linked with the Chester job since the resignation of Mark Wright.
City chairman Steven Vaughan says: "I am aware of the speculation, and the reports linking Phil with the job.
"But at the moment we have Ray Mathias as our caretaker-manager and Ray will be taking charge of the side for the two weekend games against Darlington and Boston United.
"We will obviously have to take a decision one way or the other next week, and at the moment I am not ruling anything in or anything out."
Steve McMahon, John Aldridge and Ian Rush are the other former Liverpool players to be linked with the vacancy.
