According to 60-cap Lazaridis, the job holds unprecedented cachet and kudos, with a successor to Ange Postecoglou due to be announced by mid-February amid an unprecedented wave of interest from highly credentialed candidates.
While Lazaridis and Bresciano will be at FFA HQ in Sydney in person, Schwarzer will give his insights down the line from his home in London.
Two unnamed "international experts" will also provide their input via video link, while FFA's Head of National Performance Luke Casserly, National Technical Director Eric Abrams, chief medical officer Dr Mark Jones, and Socceroos assistant coach Ante Milicic will also be in attendance.
Neither of the latter two will have a say in the final appointment.
"It's a hugely appealing job to a lot of people around the world," said Lazaridis.
"Once upon a time it was us chasing the big names because we needed a drawcard but now the big names are chasing us, and the job itself is the drawcard.
"Why shouldn't there be big names linked with this role?
"We have qualified for four successive World Cups, and the eyes of the world are on us.
"The job can be a springboard for somebody, or it could be a matter of rejuvenating an already high profile career.
"It can also be a great job for an Australian coach to carry on Ange's way.
"There are lots of possibilities."
Lazaridis is unsure what format initial discussions will take, saying the views of the former Socceroos trio would be canvassed but he wasn't certain how influential they would be in the final decision-making process.
"I am sure FFA will listen to us but they might say 'thanks for the insight but we will deal with it in our own way'.
"I think that's how it will most likely be. We are the first line and then there's Eric Abrams and Luke Casserly and then it will obviously go to the main board.
"Who we finally get may depend on the budget (believed to be in the region of $1 million).
"Although the job is so attractive perhaps a lot of coaches will not be driven so much by salary considerations."
The likes of Luis Felipe Scolari, Sven Goran Eriksson, Jurgen Klinsmann, Harry Redknapp and Tony Pulis have all expressed interest, whilst RB Leipzig coaching director Ralf Rangnick is said to have been sounded out.
Argentine coaching visionary Marcelo Bielsa is also available after being sacked by Lille.
On the local front, Graham Arnold is a major contender along with the newly unemployed Tony Popovic.
Lazaridis has no preference in terms of whether the successful candidate should be an Australian or an overseas coach.
"For me, it's a matter of getting the best man for the job ... somebody who fits the criteria set down by FFA.
"It will involve how long they want to stay, bearing in mind the Asian Cup is coming up in January 2019, hot on the heels of the World Cup.
"Initially, I thought we maybe should have looked to a local coach to take us to Russia but with the Asian Cup also in the mix, whoever gets the job needs to be there for that.
"I would also like somebody who has an eye for identifying and nurturing young talent. I think that's a key ingredient."