Gill is the leading run-scorer in one-day internationals this year and he has forged a formidable opening partnership with skipper Rohit Sharma.
"He is certainly feeling better today than he was yesterday, so that's a positive, but the medical team is monitoring him on a day-to-day basis," India coach Dravid told reporters on Friday.
"We've got 36 hours to go, so we'll see how that goes.
"We'll see whatever decision they take. But yes, he's feeling a little bit better today than he was yesterday."
Gill has scored 1230 runs at an average of 72.35 this year and his last four innings include two centuries and a half-century.
Should he miss Sunday's match against five-time champions Australia, wicketkeeper-batsman Ishan Kishan is likely to forge a left-right opening combination with Rohit even though KL Rahul also remains an option for the tournament hosts.
