Former world number one Woods is this week making only his second competitive outing since undergoing back surgery in March.
The 14-times major champion is outside the automatic nine places for the Ryder Cup match against holders Europe at Gleneagles and looks like he may have to rely on being one of the captain's three wildcard selections.
"If he's playing well and he's healthy I'll pick him," Watson told reporters at the British Open on Monday.
"But then the caveat is if he doesn't get into the FedExCup, what to do then? That's the question I can't answer right now."
Woods is a lowly 72nd on the Ryder Cup points list and needs to start stringing together some good results, starting at Hoylake this week.
"I could ask Tiger, 'how are you feeling?, are you hitting it well?," said the 64-year-old Watson. "But that doesn't mean anything really.
"The performance means something. I'll be watching Tiger and I want him on the team.
"He's a tough competitor and he's great in the team room. Wouldn't you want him on your team?".
The lucrative four-tournament playoff series kicks off with The Barclays event in New Jersey from Aug. 21-24 and ends with the big-money finale, the Tour Championship in Atlanta from Sept. 11-14.
"I hope he's playing well enough where he gets in the FedExCup and plays a few tournaments in that," added Watson.
"That's my sincere hope, that he plays well. I suspect he'll be there."
The 38-year-old Woods may be out of form and short of competitive practise but Watson said he was still capable of winning his 15th major this week.
"Why can't you understand that Tiger might very well win this tournament?," said the Ryder Cup skipper.
"I wouldn't write off Tiger Woods for a long time, the way he plays the game. He's had some injuries and other issues but the thing is he's had a long career and I fully expect it to be a longer career."
(Editing by xxx)
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