City started the season a week late after the Football Association initially refused them permission to play following a controversial takeover during the summer.
Owner Stephen Vaughan put the club into voluntary administration in May, following their relegation from the Football League, and then was part of the family consortium that bought back the club.
Chester have been in discussion with the Football Conference, the Football League and the Professional Footballers Association for a week.
A Conference statement said any decision over the club's future had been delayed to allow the Football League to consider the case.
"The club has, however, been duly informed that unless it complies in full with the conditions of membership it agreed with the Football Conference, the competition will move to consider the club's expulsion," it said.
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