Harris hit 143 for Victoria at the Junction Oval on Tuesday, bringing up his 28th first-class century just after tea before the hosts went to stumps at 7-330.
His runs came as part of a mega 239-run third-wicket stand with Peter Handscomb, who was out for 129, with national selector Tony Dodemaide in attendance.
Australia's selectors face several big decisions around the opening role in the next six weeks ahead of the first Test against India in Perth.
Most crucially they must determine if Steve Smith stays there or whether they would prefer he move back down the order to No.4.
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Cameron Green and Travis Head could both loom as options to move to the top in Smith's place if required, keeping the playing XI the same as last summer.
Any chance of Head moving, however, appeared to decrease with the left-hander listed to bat at No.4 for South Australia against NSW in their Shield game.
A timeline on Green's return from a back injury is also expected later this week, with fears he will be unable to bowl at all this summer.
Green could potentially play as a batter if deemed fit enough. Selectors would need to have faith in Mitch Marsh's body to handle the burden of being Australia's fifth bowler.
Alternatively, Michael Neser and Aaron Hardie are leading options should selectors want to bring an allrounder into the team in place of Green, giving them bowling depth.
The final option would be to move Smith back to No.4 and bring in a specialist opener, if Green is not the preferred option or considered unfit for selection.
That is where Harris, who starred on Tuesday as Cameron Bancroft copped a first-ball duck, and Matt Renshaw, who is back opening for Queensland, could come into the conversation.
Michael Neser celebrates the wicket of Cameron Bancroft with the first ball of the match against WA. (Richard Wainwright/AAP PHOTOS)
"Everyone keeps asking me (about Test chances)," Harris said.
"Probably in the past, it's weighed on my mind a lot more than what it is at the moment."I'm just playing it as it comes at me. Last year was a good lesson for that. I don't know, 'll just keep playing whatever I'm playing and trying to put runs on the board."It's always helpful if you get runs early in the season, to sort of kick-start your season a little bit. But I'm just focused on what I'm doing here."
With Victoria losing two early wickets to Gabe Bell (3-44), Harris got through a difficult early period and was chanceless until his dismissal.
The left-hander's driving on the up and to fuller balls became a feature of his innings, getting off the mark when he drove Lawrence Neil-Smith to the boundary.
He brought up his 50 inside 70 balls with a back-foot punch through the offside, before reaching three figures when he reverse-swept Matthew Kuhnemann.
Harris went after the bowling in the final session, clearing the legside boundary on successive balls to start Kuhnemann's next spell.
But he perished later in the over, trying to take the spinner on again but caught at midwicket.
Harris' most recent Test for Australia was during the 2021-22 Ashes. He held a national contract last summer before falling off the list this season.
Handscomb was also impressive, after a county summer in England in which he averaged 65.45 and was Leicestershire's leading run-scorer.
He brought up his century off 201 balls when he guided Webster to the third-man boundary, but was caught and bowled by Bradley Hope later on.
The Victorian played all four Tests on Australia's tour of India last year, and would loom as an option for the two Tests in Sri Lanka after the Border-Gavaskar Trophy.
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