Hazlewood and fellow quick Sean Abbott both left NSW's Sheffield Shield game with Victoria on Wednesday for hamstring scans after bowling in the first session.
The pair both walked to a nearby clinic and were spotted moving without a limp, before returning to the SCG as the Blues stumbled towards defeat.
Cummins was also in attendance at the SCG on Wednesday before speaking at Cricket Australia's NRMA sponsorship extension, and said Hazlewood was in good spirits.
"Joshy was pretty confident when he walked out, so hopefully shouldn't be too much of an issue," Cummins said.
"Sean I'm not so sure about. I think they're still assessing him.
"(Josh) knows his body really well. I think he was a little bit worried, wanted to get it checked out. I only saw him briefly, but he was a bit happier afterwards."
Any soreness for Hazlewood would still be of significant concern, given Cummins will miss the series opener as he returns from his own back injury.
Scott Boland will replace Cummins in the XI, but Australia have not entered a Test without two of their big-three fast bowlers since December 2022.
Hazlewood has battled a number of injuries through that time, including missing three Tests last summer with side and calf strains.
If he was to miss, Brendan Doggett would likely debut.
Doggett has taken two five-wicket hauls since returning from a hamstring injury for South Australia, and is one of the form bowlers in the country.
"He's been bowling really well the last couple of games from what I've seen," Cummins said of Doggett.
"He's really well placed to be vying for a spot in that first Test. It's always nice to have a squad full of people in form, and he's certainly one of those guys."
Meanwhile, Cummins said he was feeling well after bowling at 90 per cent on Tuesday in the SCG nets and is a chance of playing in the second Test at the Gabba on December 4.
Otherwise the third Test in Adelaide starting on December 17 looks more likely, with Cummins having also previously conceded back-to-back Tests could be difficult.
"(The Gabba) is what we're building towards," Cummins said.
"Hopefully by Perth I'm up there near 100 per cent, and then see where we're at.
"It's still pretty aggressive, going from nothing to trying to get ready for a Test match in four weeks. But we're going to give it a good shot."
Abbott is the other back-up paceman in the Test squad, but he also now appears to have some injury concern.
He took three wickets in six balls for NSW on Wednesday before leaving the SCG.
The injury scares could also place more importance on Cameron Green's fitness for the first Test, and whether Beau Webster remains in the side as a second allrounder.
Green sent down eight overs in the first innings in Perth on Tuesday at good pace, in what was his biggest bowling output in a match since before his back surgery last summer.
Webster also took eight wickets for the match in Tasmania's Sheffield Shield loss to South Australia this week, but is fighting to keep his spot in the Test side as selectors consider going with specialist opener Jake Weatherald.
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