Love announced the selections of Rickie Fowler, JB Holmes and Matt Kuchar for the playing line-up at a media conference on Monday, with the captain to make one more pick following the conclusion of the Tour Championship on September 25 to club the US line-up.
Kuchar playfully suggested it could go to Woods, who last week announced his intention to return to competitive action at the Safeway Open in October having been out since August 2015 with a back injury.
But Love, who underwent surgery on his hip in July, denied the 14-time major winner will be his final pick in a light-hearted manner.
"Tiger and I are in a race to see who's going to be the most fit for September. He and I are comparing how stiff our swings are right now and trying to get ready," he joked in an interview on Sky Sports News.
"We are both excited about the new season. Obviously he made an announcement that he's going to try and play three times in October, November, December – we're excited about that.
"You might see him and me on the side over there hitting some balls and trying to get ready. I think that he and I are both out of the running for this last captain's selection – we're a little rusty."
Woods will be present when the competition begins on September 27 having been selected as a vice-captain, and Love is confident he will offer plenty to the team in that role.
"We are going to be excited to bring him, though, excited to have Tiger Woods at a Ryder Cup. He's going be a great inspiration to our team just like [other vice-captains] Tom [Lehman] and Jim [Furyk] and Steve [Stricker] will be," he added.
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