Clarke tweaked his left hamstring during Australia's first training session on Friday, but jogged several laps on Saturday to lend hope that he may recover in time.
However with a higher-profile game against South Africa to follow on Wednesday, it is possible that Clarke will be left out of the Zimbabwe clash as a precaution, in which case George Bailey would lead Australia.
"He's better than he was on Friday, so he's probably 50-50," coach Darren Lehmann said after training on Saturday.
"We've got enough depth in our squad to chop and change if we need to, so we'll just put the best side we possibly can out to win the game."
Also Read
Should Clarke be left out on Monday, then top-order batsman Phillip Hughes could take his place after coming into the squad following an injury to Shane Watson.
Although Lehmann was yet to identify his preferred bowling attack for the game, he confirmed that it would be led by left-arm fast bowlers Mitchell Johnson and Mitchell Starc.
"Otherwise we've got some pretty good young kids as well, so it's going to be a good attack."
After using 16 players during a three-match ODI series against South Africa in Bulawayo this week, Zimbabwe coach Stephen Mangongo believes he will be better placed to field a side that can be competitive.