Harris brought up his 28th first-class century just before tea on Tuesday, and went to the break on 110 not out with Victoria 2-208 on day one after being 2-21 early.
The former Test opener's runs came as part of a big third-wicket stand with Peter Handscomb, who was unbeaten on 88 at tea.
The century was Harris' seventh at Junction Oval, with national selector Tony Dodemaide among those in attendance.
"The plan for all of us is to get him back in the Test team."— AAP Sport (@AAPSport) New @qldcricket coach Johan Botha has challenged opener Matthew Renshaw to make things awkward for @CricketAus selectors. The Sheffield Shield season begins today!https://t.co/383C0RJ5JZOctober 7, 2024
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 whether Steve Smith holds onto the role as an opener, or whether they would prefer he move back down the order to No.4.
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 on Tuesday 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 throughout summer 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.
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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, would hope to come into the conversation.
With Victoria losing two early wickets, Harris got through a difficult early period after the hosts were sent in to bat.
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' 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.
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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