Australia travelled on Friday to face Switzerland at noon on Saturday (5am Sunday AEST) at Snapdragon Stadium and depart at night after the game to return to their Bay Area base.
Volpato, who declared for Australia after defecting from Italy days before squad selection, didn't play against Mexico, but will clearly be involved.
"He's fit and available so we expect that he'll get some minutes," Popovic said, while unwilling to disclose whether Volpato would start or how much he would play.
"... He's been a bit behind with his fitness, but he looked quite good today, probably the best he's looked, I'd say, in terms of free, in terms of his movement."
Popovic said Volpato had settled into the camp well.
"He's fine. He's a good player, good young player, talented, good young man," Popovic said.
"... We've just got to get him fit. He hasn't played a lot of football, and he had eight to nine days off before he joined us, so comparing to the group, he's probably at the bottom in terms of his conditioning right now.
"But he's working hard, he's trying to get up to speed, and we've seen some good inroads in the last couple of days."
Midfielder Connor Metcalfe said it had been "smooth sailing" and batted away a question regarding whether Volpato's late change of allegiance had been an issue within the squad.
"We're all here for a reason, and I think he's here to help us get and achieve those things. So I mean, whatever's said is done, so it's fine," he said.
Metcalfe praised Volpato's "flair", quality and dangerous left foot and said he just needed to adapt to how Australia plays.
The Socceroos' final friendly before the World Cup is a dress rehearsal for Australia's second group match against the co-hosts on June 19 (June 20 AEST), with a similar midday kick-off and quick exit afterwards.
"That's what we're trying to do," Popovic told AAP.
"The 12 o'clock kick-off is a unique time - unique for food and unique for travel and playing.
"I suspect the temperature will be a bit cooler when we play in Seattle, which will be good.
"So, a good dress rehearsal, good last hit-out for players to get minutes in before the big dance in front of us."
Metcalfe said players had trained at 12pm this week and had to adjust their routines.
He added: "But they have to do it as well, so I mean it's fair game."
Popovic, keen to get minutes into players, is using the friendly to get to grips with the "four quarters" created by drinks breaks.
Tete Yengi could also debut with Popovic indicating the Socceroos had been managing him after a heavy load at Japanese club Machida Zelvia.
Switzerland pose a perfect warm-up for Australia against a European opponent before their June 13 opener against Turkey in Vancouver.
The game follows last week's 1-0 loss to Mexico, where a sluggish start proved costly before they responded in style.
Australia and Switzerland have only played once, a 0-0 firendly draw in St Gallen back in 2010.
AUSTRALIA V SWITZERLAND:
Saturday June 6, 12pm (Sunday June 7, 5am AEST)
Snapdragon Stadium, San Diego
World rankings: Australia 27, Switzerland 19
Highest ever ranking: Australia 14 (2009), Switzerland 3 (1993)
Lowest ever ranking: Australia 102 (2014), Switzerland 83 (1998)
Coaches: Australia, Tony Popovic; Switzerland, Murat Yakin.
