Hazlewood and Abbott were spotted leaving the SCG together during day three of NSW's game against Victoria and going to a nearby clinic.
It's understood the pair were able to walk the 300 metres up the road from the SCG themselves, and were not moving with an obvious limp.
Neither Cricket Australia or Cricket NSW could confirm the specifics of the injury concerns on Wednesday.
Any injury to Hazlewood would be of significant concern with the first Test against England in Perth just nine days away.
Australia are already without their captain Pat Cummins for at least the series opener, with the quick expected to be replaced in the XI by Scott Boland.
The hosts have not entered a Test match without at least two of Cummins, Hazlewood and Mitchell Starc in the side since December 2022.
Hazlewood has battled a number of injuries through that time, including missing three Tests last summer with a side strain.
If he was to be ruled out, 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.
The South Australian was initially part of Australia's squad for West Indies and would have been a chance to debut there, before suffering a side strain.
Abbott is the other back-up paceman in the Test squad, but he also now appears to have some injury concern.Â
He took three wickets in six balls for NSW on Wednesday before leaving the SCG to be assessed.
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 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.
Selectors will likely weigh up whether to play Webster in Perth as an extra bowling option, or go with Jake Weatherald as a specialist opener with Marnus Labuschagne at No.3.
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