However, the right-hander is not in any doubt for the ODI series opener against India on Sunday, cricket.com.au has reported.
The norm of resting a few seniors during warm-up games is not uncommon.
All-rounder Hilton Cartwright missed Monday's training session due to illness and is also in doubt, with a decision on his participation to be made tomorrow morning.
Finch had injured his calf playing for Surrey in England six weeks ago and has been working closely with physiotherapist Alex Kountouris over the past two days in order to be fit for Sunday's series opener.
All fit members of Australia's squad are expected to play some role against President's XI as the match is not an official List A fixture meaning each team can field more than 11 players.
Meanwhile, the Board President's XI captain Gurkeerat Singh Mann told reporters ahead the game that he was excited about playing the Australians. '
"I am excited to play. I made my debut against the Australians. Am happy to get an opportunity to play them again," he said.
Despite having little time to practice and plan, he said the players were ready.
"You need to be ready all the time. All of us have been playing. I have been playing back home. It is also a good opportunity for us to get runs/wickets and carry forward the form to domestic cricket," Mann said.
"Wherever you get selected, you need to perform. It is about giving our best. We need to keep it simple and perform to our potential," the all-rounder, who has played three ODIs for India said.
The team's coach Hemang Badani, a former India cricketer, said it was a good opportunity for the team members to get runs, get wickets and also get noticed by the selectors.
"They are all professionals and are ready to go. It is a great opportunity to play against international opposition and if they perform they will get noticed," he said.
Badani recalled his personal experience several years ago when he was out of the national side and scored a ton against New Zealand to win back a place (in the ODI team).
Aaron Finchaustraliaaustralia vs board's president xiind vs aus 2017India vs Australia 2017warm-up tie
First Published: September 11, 2017, 5:09 PM IST