Melbourne Victory coach Ange Postecoglou has firmed as the bookie's favourite for the Roos job in the last 24 hours, ahead of Central Coast Mariners' Graham Arnold and Western Sydney Wanderers' Tony Popovic.
Now Lowy has said he hopes to follow through on a promise to appoint an Aussie when sacked Holger Osieck was given the hot seat in 2010.
"When we appointed Holger coach three years ago, I recall I said words to the effect 'I hope the next coach will be an Australian'," Lowy said today. "That was the plan and is still the plan.
"Our preference is clearly for an Australian coach. Three names are being talked about and it's not wrong that we have three possible Australian candidates."
The likely outcome will mean an A-League club loses its coach in the middle of the season to give the new Roos coach the maximum amount of time to focus on the World Cup campaign.
"The dilemma we have is how to keep the balance because the season has just started and the clubs have worked very hard to set themselves up," Lowy said.
"So it's up to us to find a way to negotiate with whoever we pick and see what can be done so as not to disrupt their plans.
"One club may be more reasonable than another and we need to be mindful of that, after all the A-League is doing extremely well. It will be a joint discussion, the club has to have a big say in what they are prepared to do. 
"Hopefully we will come to terms with one of those three, and failing that we'll need to find somebody else from overseas."
He added:  "We will have an intensive, short process in place, I hope in a week a two. Our objective, if we find the right person with the right qualifications, is to go beyond the Asian Cup.
"I think we're wiser now than we were three years ago. I would expect that we would talk to the coach and make up our mind whether he will fulfil the criteria that we put to him.
"But once we appoint him we can't tell him what to do. We want to have a credible performance at the World Cup and win the Asian Cup. That was our goal then and that is our goal now."