Later this week, however, the pair will collide as arguably the hottest two players in golf when the US PGA Championship tees off at Bethpage Black on Long Island.
Woods, 43, won the US Open at the same New York venue 17 years ago but returns as the Masters champion after a remarkable win at Augusta in April.
The big-hitting Koepka, 29, is a triple major champion in his own right having won three of the last eight majors, including last year's US PGA, when he fought off a resurgent Woods to secure a two-shot triumph at Bellerive.
That he finished tied for second at Augusta last month merely reinforces his status as a man at the top of his game. For Koepka, a charging Tiger holds no fear.
'I'm not afraid of anybody,' he told CNN Sport. 'There's no reason to be afraid of anybody. We just know now that he's more than likely going to be there come Sunday.'
Koepka's recent run is a phenomenal feat that separates him from his equally illustrious peers; Jordan Spieth's trio of major titles came in an 11-tournament period, while there were 15 majors between Rory McIlroy's first and fourth wins.
Now, though, there is an added complication for the game's Generation Z to consider; during his absence, many admitted that they would have loved to have witnessed -- and gone up against -- Woods in his prime. At the Masters, they were treated to a blast from the past.
'Good for the game'
But as the defending US PGA champion, Koepka is happy to be the hunted, rather than the hunter.
'I love it,' says world No. 3 Koepka, a straight-talker, whose bulging biceps are the hallmark of the modern golfer.
'I think it is an honor to have that extra little status of defending champ. It is what you gear your whole year around and that is something I enjoy. I enjoy the added pressure. I enjoy everything that comes along with it and I try to focus in on it and making the best of those weeks.'
Koepka co-led the Masters through the first two rounds and was right in contention on the back nine on Sunday until his charge faltered as one of several players to find the water of Rae's Creek on the short 12th.
At the end of it all, one shot was the difference. Woods clinched his first major for 11 years and was mobbed by an adoring Augusta crowd, and greeted by colleagues and rivals as he approached the clubhouse.
High-fives, backslaps, ceaseless whooping -- the respect and shared joy was plain to see. Then Koepka tapped him on the shoulder for a bear hug between recent friends.
'I've seen him when he was not able to play golf and not sure whether he was going to be able to get back to playing golf,' he reflects of their embrace.
'It has been interesting, it has been a fun journey to watch. Everybody wants him out there again. He's back healthy and it has been fun building a friendship over the last couple of years.
'It is just good for the game. I think it's good for the fans, the sponsors, the events. It's good for the tour, it's good for the players, it's good for everybody that he's winning. As players, we all knew that he was back a long time ago.'
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Koepka was speaking after taking part in a trick-shot challenge with US beer brand Michelob ULTRA. By landing an approach on a floating green on the Hudson River, he won a free drink for all the people of New York City. 'I'm a popular man right now,' he laughs.
Pressure situations such as these are where he thrives.
'Every time I tee up, I'm trying to win,' adds Koepka, who has finished in the top 20 in all but three of his major appearances since 2015.
'I've done a good job of it in the majors in the last few years in terms of understanding what I do really well.
'Big-time players are going to show up in the majors and that's where you want to give yourself a chance to win it -- with nine holes to go. It is a lot of patience and hanging around, because you can't win it in the first three days.'
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This year's US PGA, however, includes a fascinating subplot.
From now on, the tournament will take place three months earlier than before -- partly to assist golf's place at the Olympics, while also allowing southern US states to host the tournament in cooler temperatures -- meaning the major calendar will be complete by the fourth week of July.
'It is interesting now because, literally, if you get hot you could run off all four majors in a four-month span,' says Koepka.
'If you're going to play good, now is the time to do it because they are all so close together. The players like it -- it has been very well received.
'For Tiger, having won, I'm sure he loves the fact that this is happening now because he's playing good.'
The revised format could well assist Woods' goal of chasing Jack Nicklaus' record of 18 major victories, but for Koepka it changes nothing.
'I couldn't care less what anybody else is doing,' he says. 'I'm not there to see how other guys are hitting it. When you start worrying about everybody else, that's when you start becoming a little distracted.
'I'm there for one reason only. I'm there to play. I'm there to win.'