Antic was not immediately available for comment but the reports said he wanted two million euros in compensation for last month's dismissal after Serbia's opening two Euro 2012 qualifiers.
FSS president Tomislav Karadzic said he was certain the 61-year-old coach had no chance of winning a legal case if the matter went to court.
"Antic can sue us if he wants to but we are convinced that justice is on our side and that he stands no chance of winning the case," Karadzic told Reuters by telephone.
"But even if Antic somehow gets it to go his way, the financial loss we might suffer would be a small price to pay to close the chapter on him.
"My advice to Antic is to look for another job, if he can get one in Europe given the fact that he was in the wilderness for four years before he coached Serbia," Karadzic added.
Antic, who won the Spanish league and cup double with Atletico Madrid in 1996, took over as Serbia coach in 2008.
His acrimonious split with the FSS came during a four-game touchline ban imposed by FIFA after Antic insulted the referee following Serbia's 2-1 World Cup defeat by Australia which knocked them out in the group stage.
Antic was initially allowed to keep his job after taking a pay cut but was axed following Serbia's 1-1 Euro 2012 qualifying draw with Slovenia, when his deputies replaced him in the dugout.
Antic's contract stipulated he could be fired without compensation if he was "unable to perform his duties through any fault of his own."
The FSS argued that the FIFA ban disqualified Antic from doing his job during Serbia's 3-0 Euro qualifier win over the Faroe Islands and the Slovenia draw, with the coach watching both games from the terraces.
But Antic's lawyers replied he did not have to be in the dugout to do his job, having been in charge for training sessions and team selection before the matches.
Serbia, now coached by former Arsenal midfielder Vladimir Petrovic, play Estonia at home on Friday and Italy away on Tuesday in their next two Group C qualifiers.
