FIFA has given the ASF until January 13th to enforce a transfer ban on Sion after the Court of Arbitration for Sport (CAS) upheld a UEFA decision to refuse the club re-entry to the Europa League.
The club has written to the ASF asking that it appeal against the suspension, a statement on the Sion website said.
"It is obvious that this ultimatum respects neither the statutes and rules of FIFA nor Swiss law," it said.
"Sacrificing" the club to satisfy FIFA would show a lack of courage and put in doubt the ASF and the Swiss Football League's ability to continue managing Swiss football, the club added.
Following the suspension warning earlier this month, the ASF said it did not believe any FIFA regulations had been broken and would defend its position with an appeal to CAS if necessary.
The row erupted after Sion, the subject of a transfer embargo over the signing of Egyptian goalkeeper Essam El Hadary, proceeded to sign six players in the summer.
The club then fielded five of the six players during a Europa League play-off tie against Celtic earlier this year and were kicked out of the competition as a result, with UEFA's decision to expel them upheld by the CAS.