Khawaja struggled with back spasms during Australia's dramatic victory over England in the series opener in Perth, failing to open either innings and contributing only two runs to his team's cause.
Travis Head's match-winning century as Khawaja's replacement as opener has reinvigorated the debate over the top of the Australian order, but Labuschagne bridled on Monday when asked if he had any advice for the lefthander.
"I don't think he needs advice," Labuschagne told reporters at Brisbane's Gabba, where the second test starts on Thursday.
"He's 38, he's been around the block a long time ... he's an amazing player.
"And the way he's gone about his game, the way he's gone from a number three, four and then to open the batting, and the way he's done that and navigated some tricky scenarios. He's just been awesome.
"So I don't have any advice for him on it, because ... in first-class (cricket) this year, he's batted beautifully.
"The way he's been batting is awesome."
Ironically, the heated debate about Australia's opening partnership over the 22 months since David Warner retired from tests has previously focused entirely on who should bat with Khawaja.
Labuschagne and Steve Smith have filled the gap left by Warner on a temporary basis but the 31-year-old suggested on Monday that the time for such experiments was over whatever was decided about Khawaja.
"I think we can pretty much be sure that Steve or I won't open," he said.
Labuschagne, who normally bats at number three, was dropped from the test side during the tour of West Indies in June and July after a poor run of form only to storm back into the team with a string of centuries in domestic cricket.
In Perth, he scored a modest nine runs in the opening innings before securing his 24th test half-century in the company of Head to get Australia across the line for an eight-wicket victory.
"I personally took a lot away from that," he said.
"To be able to go out there and finish the game off, build that partnership with Trav and be able to play some really free-flowing cricket was really exciting."