Antic was handed the ban for insulting the referee after Serbia's 2-1 World Cup defeat by Australia and FSS president Tomislav Karadzic said the 61-year-old's coach's fate was now hanging in the balance.
"The FSS executive board will convene and make a decision in the next two days because we need to know who is going to be in charge before the Euro 2012 qualifiers start," Karadzic told Reuters on Tuesday.
"I am keeping an open mind and I would hate to lose Antic because he is the best coach we have got, but the executive board is a body of experts and former coaches who will have the final say.
"It is a difficult situation because if Antic stays it means we will have to play our opening four qualifiers without a coach and if we part company, his legacy will be the tremendous progress Serbia have made during his two-year spell in charge.
"There is still a chance that Antic might stay at the helm but I don't want to make any speculations at this point."
Antic steered Serbia to the World Cup in South Africa - their first major tournament as an independent nation - but the team failed to live up to expectations, bowing out in the group stage of the competition.
PAY CUT
Karadzic then said Antic would have to take a pay cut if he wanted to carry on and calls within the FSS for the coach's dismissal intensified after the FIFA ban.
Should they fire Antic, the FSS will most probably be forced to pay him a heavy compensation fee because he has two years left on his lucrative contract.
"I am not bothered because I have given my entire self to Serbian soccer but the negative atmosphere has affected the players," Antic, who has been given unanimous support from the players, told a news conference on Tuesday.
"I have a rock-solid contract and I trust my agent because he is a top-level professional, so if the FSS want to get rid of me they will have to honour it to the last letter.
"The players and staff have grown on me since I took over, we have become one big happy family and I am absolutely overwhelmed by their support in these turbulent times.
"I don't think this will be my last game in charge but it's not my decision, either way I would like a full house because we are up for an entertaining game of football."
Serbia start their Euro 2012 qualifying campaign in the Faroe Islands on Sept. 3 and are at home to Slovenia four days later.
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