Golf's third major of the year begins at Pebble Beach on Thursday, with Woods among the top contenders after winning the Masters in April, ending an 11-year major drought to claim his 15th.
Victory for the 43-year-old would see him tie Nicklaus and three other players on a record four U.S. Open crowns.
He is now only three overall majors adrift of Nicklaus, who thinks the gap could become two at the venue where Woods won the same tournament by 15 strokes back in 2000.
"I would think Tiger [Woods]," Nicklaus told Sky Sports when asked who was the favourite this week.
"Tiger won there by a million the last time he won and he grew up around that area.
"He is smart, so knows how to play there, so I think Tiger will play well.
"But a lot of the guys are playing well too, so it will be a good tournament."
Oh hey... Remember a certain Sunday here 19 years ago? pic.twitter.com/OypkH70GlJ
— U.S. Open (USGA) (@usopengolf) June 10, 2019
Nicklaus warned all the players they would have to be on guard at a course where you can quickly find yourself in trouble, as Brooks Koepka looks to defend his 2018 title and add to his US PGA Championship won last month.
"Pebble is not a long golf course," added Nicklaus. "Length is not the big issue there, the issue is being smart and not putting yourself in a position where [you can have] a double-bogey - it happens real quickly at Pebble Beach.
"You have to put yourself in a position to take advantage of a hole when you can.
"The greens are tough to make putts on, but the guys have played a lot there and understand a little bit about what goes on there.
"If I had one round of golf to play that that's where I've always said that where I would want to go, so obviously I love Pebble Beach too. I won the Amateur there and quite a few other things, so it has had a special place in my heart."
Woods finished in a tie for ninth at the Memorial Tournament in his last outing a week ago.
Photo Getty Images. Caption: Tiger Woods at the Memorial Tournament