Queiroz questioned over insults
"The facts that have been discovered in an inquiry oblige the federation to ponder them," Dias told Radio Renascenca. "If they were not grave facts there would not have been an inquest or it would have been archived."
Queiroz guided Portugal to the second round of the World Cup finals in South Africa last month, where they were knocked out by eventual winners Spain.
"It is an extremely delicate matter, which the FPF will analyse in depth and will inform on at an opportune time, after having heard all the parties," the federation said in a statement.
The federation last week said Queiroz's team had met its minimum target by reaching the second round and that he would remain as coach for the next two years, but local media said the inquest could raise calls for him to leave the job.
The Diario de Noticias daily reported on Friday that an initial inquiry had revealed Queiroz had allegedly insulted Luis Horta, president of the Portuguese Anti-Doping Authority, and doctors from his organisation when they visited the Portugal squad in Covilha to test several players.
It added that all of the players passed the tests, but Queiroz was allegedly angered by the unexpected interruption of the squad's training programme.
The FPF is expected to formally announce next week the opening of an inquest, which will be handled by its disciplinary committee, the newspaper said.