Gallop said he was seeking to find a replacement - preferably before the November international dates - for Holger Osieck, who was sacked hours after the Socceroos crashed to a 6-0 defeat to France in Paris.
"It's fair to say that feelers have been put out, but nothing more than that," Gallop said.
Gallop said Osieck was informed of his dismissal at the team hotel shortly after the match, Australia's second successive 6-0 loss in five weeks.
Hiddink, Marcelo Bielsa and Gerrard Houllier have been linked with the vacant role while Australian coaches such as Ange Postecoglou and Graham Arnold are also believed to be in the frame.
Gallop said it was the long-term preference to have an Australian coach but FFA would also consider international options for now.
He said it was inappropriate to say who had and hadn't been spoken to.
"It certainly makes sense to have an Australian coach but whether that makes sense right now, is something we need to look at seriously over the next few weeks," Gallop said.
"... It's not appropriate to go into who has been contacted and who hasn't but obviously some feelers have been put out.
"We're always exploring options and at the moment that's all we're doing.
"We'll hopefully have some definitive answers on that over the next few weeks.
"Certainly it's something we want to get along with straight away."
Gallop said whoever was appointed would have a strong focus on the Socceroos' long-term success, along with a competitive showing at next year's FIFA World Cup.
"This is about the need to rejuvenate, regenerate our team," Gallop said, adding there was an opportunity for a new coach to make significant changes before Brazil.
"We've got a lot to look forward to the next months and years.
"Obviously Brazil is important as is the 2015 Asian Cup and ultimately we want to be at the next World Cup as well. This is a decision taken in the long-term interests of the team."
Assistant coach Aurelio Vidmar will lead the team against Canada in London on Wednesday (AEDT).
Osieck was still at the team hotel in Paris on Saturday evening (AEDT) but declined media interviews.