If the suspension took effect, Swiss champion FC Basel would be prevented from playing Bayern Munich in the Champions League round of 16. The first leg is scheduled Feb. 22 in Basel.
Swiss FA leaders were meeting Saturday to weigh the FIFA ultimatum.
Sion has breached football's rules in a legal saga since 2009 when FIFA imposed a one-year transfer ban for breaking transfer regulations in the signing of goalkeeper Essam El-Hadary.
On Saturday, FIFA criticized ''the attitude of the club repeatedly trying to circumvent this decision in a legally abusive manner,'' in a statement issued after a meeting of its executive committee.
Sion's determination to fight football and legal authorities led it to launch a series of civil court actions against UEFA since being expelled from the Europa League in September for fielding players that were signed during the transfer ban.
FIFA and UEFA were backed on Thursday by the Court of Arbitration for Sport, which upheld UEFA's right to kick Sion out of the competition based on FIFA's transfer sanction.
FIFA stepped up the fight Saturday by ordering the Swiss FA to enforce a ban on registering six Sion players signed in the offseason during the transfer embargo.
''As a consequence, all matches in which the relevant players participated shall be declared forfeit or three points shall be deducted respectively,'' FIFA said. ''Should this deadline not be respected, the Swiss FA will be automatically suspended from Jan. 14, 2012 onwards.''
Under the terms of a FIFA suspension, a country's national and club teams, referees and officials are prohibited from taking part in international matches and meetings, or receive FIFA funding.