Andrew McGlashan is a deputy editor at ESPNcricinfo
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It is a conversation that may well already have taken place and Burns has had plenty of backing in recent weeks from selectors and team-mates, but two more low scores at Drummoyne Oval for Australia A - caught behind trying to leave a ball and then dragging on a drive - left him with a tally of 61 runs in seven innings for the summer.
The wording of national selector Trevor Hohns' remarks on Wednesday - where he said Burns had enjoyed "excellent" preparation and that the second Australia A match would "round it out nicely" - did not suggest a player about to be jettisoned.
"It may be the sensible thing to do, say don't worry, you are going to walk out there in Adelaide now gain some exposure against Bumrah and whoever the Indians serve up under light," Gilchrist said at a Fox Cricket BBL launch event.
"That would be a good sensible approach to clear any doubts out, that he has the backing, he's not playing a trial game, he's just having a practice game to sharpen up for Adelaide.
"Nothing ever seems to be a perfect science. You can get nicked out and go into the Test a big negative of mind because you haven't got the runs, but 10 balls into your Test innings you can that's what it feels like and you are away."
The selectors have yet to add any batting reinforcements to the squad but it is expected that Marcus Harris, who will open with Burns for Australia A, will be added as cover for Pucovski. However, they may need to consider more than one extra batsman given that very last-minute additions are still not possible under the Covid-19 protocols for the tour.
That could open the door for an experienced player such as Usman Khawaja although there was no indication that he was about to leave the Sydney Thunder BBL squad currently in Canberra.
"If you went to Khawaja, I don't think he'd see it as just one game, he'd say he'd make it hard to drop me now and eye a few more years in the Australian team," Gilchrist said. "Marcus has had some Test experience, done a lot right in the Shield season. I don't think we are bereft of strong options, just working out which is the correct one."
The second Australia A match will also be another chance for Cameron Green to impress in what will be his first experience of pink-ball cricket. It remains unlikely he will force his way into the Test side for Adelaide, but his unbeaten 125 and a brace of wickets at Drummoyne continued to mount his case. He will likely be facing Jasprit Bumrah and Mohammed Shami as they prepare for the Test series.
"I've never faced it [the pink ball] before, for whatever reason I keep dodging the day-night games in domestic cricket, so I'll have a training session today and that will be the first time I'll face it or bowl with it so that will be pretty interesting," Green said. "There's a lot of guys in the team who have played pink ball before so will try to bounce as many ideas off them as I can.
"I've spoken to a few guys, they say if you are batting at night but you are already in it seems okay, just when you are new to the crease it's very tough to get yourself in."
From the India attack he faced in the first game, he picked out the "world-class skill" of Umesh Yadav as the most challenging of the bowlers. "He was bowling down breeze on a wicket that had a bit in it so that was incredibly tough," he said.
Bowling-wise, Green said he was on track with where he and the coaching staff had hope he would be as he continues to be limited to a handful of four-over spells. He expects that level to be maintained for at least another couple of weeks before any increase is considered.