Nicklaus said Friday that Woods can achieve the feat "if he gets the five inches between his ears squared out."
"I mean Tiger has a great work ethic, he's a great competitor, the most talented kid on the planet right now," Nicklaus told The Associated Press in an interview. "He's not going to go away."
Woods has 14 major titles, but has not won any tournament since revelations of infidelities in 2009 led to the collapse of his marriage and a break from the sport. This season has been partly derailed by injuries, but Nicklaus also praised the decision by U.S. captain Fred Couples to include Woods in the 12-member Presidents Cup team that will take on non-European players in Australia in November.
"How could you not pick him," the 71-year-old legend said. "I mean he's Tiger Woods, he's the best player in the game. He may not be playing his best today, but he's still Tiger Woods."
Nicklaus made the comments while in South Korea to attend a Champions Tour event played on a course he designed in the port city of Incheon west of Seoul.
He also said it is crucial for golf to stage a successful tournament at the 2016 Olympics in Rio de Janeiro to help the game grow further internationally.
"Golf is now an Olympic sport," Nicklaus said. "And we've got to keep it in the Olympics. We've got one shot in 2016."
How successful those Olympics are for the sport is important, he said, because there will be a vote the following year to decide if it goes beyond the 2020 Games.
Nicklaus expressed concern, however, about the slow progress in constructing the facilities for the event, but remained hopeful that he will be awarded the task of designing the course together with former women's great Annika Sorenstam.
Golf is returning to the Olympics as a sport for the first time since 1904, with the tournament held in the seaside region of Barra.
A course needs to be built by 2015 when test events begin.
"I've led my game and (Sorenstam) has led the women's game and I think we both have the ability more so than anybody else to put something together that would fit what they need," he said.
Others who have expressed interest in designing the course include Arnold Palmer, Gary Player, Nick Faldo and Greg Norman, who would team up with Lorena Ochoa.
Nicklaus stressed that the Olympics will be by far the biggest sports event ever organized in Brazil, and that officials must realize they're facing a tough deadline to get things done.
"You've got to get ready for it, prepare for it. And to get people to understand the sense of urgency is very difficult," he said. "And the sense of urgency needs to be there, otherwise the success of an event is in jeopardy."
Nicklaus' many course designs around the world are part of his way to leave a legacy in the game that goes beyond his playing days. Now he's trying to add to that by giving more young people a way into the sport in a time when many families are struggling economically and lots of kids turn to cheaper and more accessible options.
He cited football and basketball as examples, where children play with modified equipment and rules, such as smaller balls and lower baskets, to make things easier.
"Kids have got to have some success, they have success early in these other sports, but they don't get this success early in golf," he said. "In golf, it's a hard golf ball, the same golf ball that the pro is playing and a hard golf club," Nicklaus said.
He added that he is working on developing equipment to help make it easier for young people to play in public parks.
"One of the things I'm working on very hard right now is trying to figure out how can we leave a legacy" so that people want to play the game, he said.