Nicklaus was warming up for the pro-am, the closest he gets to competition these days.
There are amazing parallels in their careers, from green jackets at Augusta National to the two claret jugs at St. Andrews. They were the youngest of their eras to complete the career Grand Slam. Both were 30 when their fathers died, and both went on to win the British Open that summer.
Perhaps the most glaring difference was their rivals.
Nicklaus had rivals with staying power that stretched over two decades, from Arnold Palmer to Gary Player, Lee Trevino to Tom Watson. Woods' rivals seem to come and go like fashion trends -- David Duval in 1999, Phil Mickelson in 2001, Ernie Els in 2002, Vijay Singh in 2004, nobody in 2000.
After his pro-am round at the Memorial, Woods recalled talking to Nicklaus about rivalries.
'He said that as long as you're part of the conversation over 20 years,' Woods said with a smile, 'then you're doing all right.'
Mickelson has joined the conversation again.
A week after Woods won the Wachovia Championship, Mickelson won THE PLAYERS Championship. They are 1-2 in the world ranking and on the PGA TOUR money list. Both return to action this week at the Memorial, which has a 107-man field with the focus squarely on two players.
'He's playing better, no doubt about that,' Woods said.
Mickelson has 31 victories on the PGA TOUR -- no one has more among active players except Woods -- and now is working with Butch Harmon, the celebrated swing coach who refined and then retooled Woods' swing at the start of his career.
Of all the rivalries Woods has faced, this is the most natural, even he says that his biggest rival is himself.
'I keep pushing myself pretty hard regardless,' he said. 'I always try and get better. You can't stay stagnant in any sport. You've always got to keep getting better, because you know the guys are training harder; they're refining their game.'
Asked about their renewed rivalry, Mickelson said it was flattering.
'To me, anyway,' he quickly added. 'Probably not to him, but it's flattering to me.'
Mickelson began working with Harmon right before the Byron Nelson Championship at the end of April, and the results have been on the upswing. He was third at the Nelson, third at Wachovia and won THE PLAYERS.
With the U.S. Open approaching, former U.S. Open champion Johnny Miller gives Mickelson the edge.
'I believe he's the favorite right now,' Miller said Wednesday. 'Give me Tiger or Phil right now, I'll take Phil.'
Mickelson was on top of his game a year ago, coming off his second Masters title, with Woods taking two months off to cope with the death of his father. He had a one-shot lead going into the final hole at Winged Foot, only to make double bogey and lose by one.
Woods, who had missed the cut, won the next two majors, and the search was on for another rival.
Mickelson doesn't waste much time studying the world ranking, because the gap is more of a chasm; Woods is likely to hold down the No. 1 position the rest of the year no matter what Lefty can accomplish.
And even smaller goals -- Mickelson has never won a money title or player of the year -- will take some extraordinary achievements.
'We're talking about probably the best player of all time,' Mickelson said. 'I'm working hard. I think it's going to take some time for me to get ultimately where I wanted to be, as far as where I want my swing to be, as far as where I want my ball-striking to be and my misses. But I'm certainly optimistic with the early success that I've had.'
He would like to find more at Muirfield Village, which has an impressive roll call of winners. Woods won three straight times at the turn of the decade. Other past champions include Ernie Els, Vijay Singh and Jim Furyk.
'A lot of great players have won this tournament. I have not,' Mickelson said. 'I think it's one of the tour events that I would very much like to win.'
That would ratchet the rivalry up another notch, and Nicklaus wouldn't mind seeing that. He was asked earlier in the week if it would be better for golf to have someone measure up to Woods.
'If somebody can play that well,' Nicklaus replied. 'That's all it amounts to.'