Altrincham have had 18 points deducted by the Conference and have been fined £1,000 for fielding an ineligible player earlier this season.
Robinson left Altrincham in February to move to Australia
The ruling would put the Robins bottom of the Conference and would almost certainly mean relegation.
James Robinson was ineligible when he made 13 appearances for Altrincham this season, scoring four times.
Altrincham are waiting to receive the decision in writing before deciding whether to appeal to the FA.
Robinson, 23, signed for the Moss Lane club from Accrington Stanley last November when he did not have international clearance after a spell in Iceland.
The player left Moss Lane in February to join Richmond Eagles in Australia.
"The problem only emerged because he went from us to Australia," an Altrincham spokesman said.
"The first we knew of the problem was when they (Richmond) came back to us and said they had discovered he was still registered to play in Iceland when he signed for Accrington."
The Altrincham spokesman continued: "As far as the club are concerned, the manager Graham Heathcote, and the chairman both want to speak to the players before saying anything more.
"The appeal needs to be made within two weeks, so we are expecting written confirmation of the punishment very soon."