Uncapped playmaker Burgess has led the charge with his creativity from deeper in midfield amid Newcastle's extraordinary seven-game winning streak that has the Jets five points clear on top of the A-League Men table.
The 31-year-old was frozen out at Sydney FC by Ufuk Talay last season but snapped up by first-year Jets coach Milligan, and was man-of-the-match in the Australia Cup final.
Burgess's switch from an attacking midfielder into a No.6 has proved a Milligan masterstroke.
Wearing the captain's armband, Burgess pulled the strings from holding midfield as Newcastle beat Perth 3-1 at HBF Park on Friday night.
"Obviously yes, he's probably better known as a No.10 or a wide player coming inside but we just saw attributes in him and his willingness to get on the ball and defensively as well to organise and do all the dirty stuff that the No.6 has to do as well," Milligan said.
"He's taken it on board and he leads by example by his actions and his determination to become a better player. I think Max is still becoming a better player every single day.
"Look, I don't want to put any pressures on him or anything like that but he's still only 31.
"There's a lot of football for the national team to come up and I think he's someone they should be looking at. That comes down to the hard work that he's done from the very first moment that he's walked in."
Few people are better qualified to talk about who should be considered for the Socceroos than Milligan, who has 80 caps, won the Asian Cup, went to four World Cups and captained his country.
Burgess loomed as a future star at Western United back in 2020-21 before sitting out part of a season in a bid to force a move back to Sydney.
He had moments of quality at Sydney without consistency, but has thrived under Milligan.
"He was one obviously early on I was extremely excited to get because I think he has some fantastic attributes as a footballer," Milligan said.
"From the moment he walked through the door at the Jets he's been the ultimate professional.
"He leads by example and that's what you want from your older players. There's a couple of them, it's not just Maxy - but he's taken the bull by the horns in that sense."
Once a talented, if inconsistent attacker, Burgess is loving his new role.
"Weve got Millsy who obviously had a great career as a midfielder," he said.
"So learning off him. We're a ball-playing side, so for me it's great playing a bit deeper."
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