Portuguese soccer federation president Gilberto Madail said Oliveira made the offer during an eight-hour meeting on Thursday called to consider the causes of Portugal's first-round exit from the tournament.
"Antonio Oliveira put his job at my disposal and I will make a decision on this matter within a week at the most," Madail said.
Oliveira has a contract to coach the squad through to the European championships in 2004, which Portugal is hosting.
Federation vice-president Antonio Boronha submitted his resignation during the meeting and left shortly after it started.
Madail said he would ask the head of the federation's assembly to call early elections as part of an administrative shake-up. The elections are now set for November.
Portugal, one of the favoured teams going into the World Cup, bowed out after first-round defeats by the United States and South Korea.