According to a report cricket.Com.Au, Handcomb will fly in as cover ahead of Sunday's series opener against India here.
Finch aggravated a calf injury during training here on Thursday. A scan later revealed that he would need to sit out the early part of the five-match series.
There were initial fears that the injury might rule out Finch for the entire tour, but according to the report the opener will remain with the squad with an aim to play in the later part of the series.
Handscomb, who returned to Melbourne following the recent Test tour of Bangladesh, would depart for India on Saturday and would be available for selection in the opening match of the series.
Finch was rested from Australia's lone warm-up match against Board President's XI on Tuesday due to the right calf injury, which he first suffered playing for Surrey in England six weeks ago.
The 30-year-old Victorian is expected to miss the first three ODIs.
"Aaron (Finch) re-aggravated his pre-existing calf injury during warm-up at training yesterday," the Australian team physiotherapist Alex Kountouris said.
"He has had a scan in Chennai and although we believe it is not a serious recurrence, he will not be available for the first few one-day matches here in India.
"He will remain with the squad whilst we assess the injury and establish his return to play timelines," the physio added.
The Aussies had used all-rounder Hilton Cartwright as the opener in the warm-up game. He was however, dismissed for a second ball duck.
It remains to be seen if the visitors use Cartwright or push the left-handed Travis Head up the order for the first ODI.
The first match of the ODI series would be played at M A Chidambaram Stadium here on Sunday.
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