The four-match series is tied at 1-1 after the tourists won the first test in Adelaide by 31 runs and Australia took a 146-run victory in the second test in Perth.
"It's a long series, our bowlers have had a really big workload and we feel we're going to need Mitch's bowling at some point," Cricket Australia's official website quoted Paine as saying on Tuesday.
"I'm sure Pete would be upset. I think he's had conversations with the selectors that there's a few things they would like him to work on and Pete is open to that."
Number five Handscomb, who scored a combined 68 runs in four innings so far against India, still had a future as a test batsman, added Paine.
"Pete at his best is going to score a lot of test runs and not just his batting, he brings a hell of a lot to our side in terms of his fielding, his experience and just the way he generally goes about his cricket," he said.
"We're sure he'll score a lot more runs for Australia."
On Monday, Australia coach Justin Langer had endorsed Marsh's potential value on a pitch that tends to test the bowlers.
Forecasts for warm weather and only three days' gap before the final test in Sydney also means Australia are keen to be extra careful about managing the workload of their frontline pacemen.
Australia team: Aaron Finch, Marcus Harris, Usman Khawaja, Shaun Marsh, Travis Head, Mitchell Marsh, Tim Paine (captain), Pat Cummins, Mitchell Starc, Nathan Lyon, Josh Hazlewood
(Writing by Peter Rutherford in Seoul; Editing by Michael Perry)
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