Clarke will miss Australia's remaining three one-day internationals against South Africa due a hamstring injury linked to his long-standing back issues.
Conflicting messages from the Australia camp have seen separate backroom staff members claim Clarke will either be fine to face India in Brisbane or could require surgery.
Test opener Watson, himself on the comeback trail after a calf injury, had positive news on the skipper when facing the media ahead of Wednesday's third ODI against the Proteas.
"The diagnosis is, I think, better than what it was initially, which is a great thing. It's all very positive," Watson said.
"Hopefully, over the next week or so, it'll continue to improve really well and he'll be right for the first Test."
"If he's fit it'd be a great thing, he's got an incredible record as a captain but also as a player as well.
"Everyone's preference is for Michael to be captain and be fully fit for that first Test match because, certainly as a leader, it'd leave a hole but as a player as well."