Watson is allowed three at-large selections to fill out his 12-man team that will play against Europe in September at Gleneagles in Scotland.
The problem for Woods could be a lack of opportunities. After this week's Open Championship at Royal Liverpool, he is expected to play the WGC-Bridgestone Invitational and the PGA Championship, the last qualifying event.
That is also just one week prior to the cutoff for qualifying for the PGA Tour's FedEx Cup playoffs, the four tournaments that lead up to the Ryder Cup. Unless he has a couple of high finishes, Woods is unlikely to qualify for the playoffs.
"It's performance," said Watson, who is expected to meet with Woods this week. "I could ask Tiger, 'How are you feeling? How are you feeling like you're hitting the ball? Are you hitting it well?' And that doesn't mean anything, really. The performance means something. I'll be watching Tiger and I want him on the team. I do. He's a tough competitor and he's great in the team room. Wouldn't you want him on your team?"
Woods has played just two competitive rounds since returning at the Quicken Loans National following back surgery on March 31. The Open is his first major championship this year.
Woods did not play a practice round on Monday after getting in 12 holes Saturday and 18 holes on Sunday.
"He was impressive," said Matt Kuchar of their Sunday practice round together. "I thought he was crazy to come back as early as he did but he said he thought it was the right thing to do, to test it and see how fit he is. He said he's recovering well, that after playing he gets up the next day and feels good.
"We had a little match going and on the last hole he duly stuffed one in there from 160 yards to beat me, so that was a bit of a bummer but totally like the Tiger we're used to seeing."
Watson, who won the Open Championship five times, is playing the tournament for the 37th time. He recently had his exemption extended by the R&A for one more year so he can celebrate the 40th anniversary of his first Open and perhaps play his final one next year at St. Andrews.