Woods, who surpassed the record total of weeks as world number one on Monday with his 332nd week in the top spot, is under increasing pressure from newly-crowned U.S. PGA champion Vijay Singh and world number three Ernie Els, both of whom are playing at the Firestone Country Club in Akron.
The 28-year-old American has held the number one spot for a record 262 consecutive weeks, though that lead has been slowly whittled away by Singh -- who won his third major in a playoff at Whistling Straits on Sunday -- in the last 12 months.
"I said in the beginning of the year that my goal before I finish playing should be to finish number one," said Singh.
"I want to finish number one. I want to be the number one player in the world.
"I've won five events this year. I won four last year ... and I'm doing the best I can to get that position."
One of the factors that has counted against Singh attaining the number one spot, despite winning more consistently than Woods in the last 12 months, is that he plays more events -- something he is acutely aware of.
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"I have more points, I won more tournaments. I think my average is still pretty low. It just doesn't get to a point like Tiger or Ernie's.
"They've got to come up with a system where playing more doesn't matter."
Woods, however, said he was not as concerned about the number one ranking as he was about maintaining his remarkable cut streak. He made his 129th successive cut at the U.S. PGA last week, before finishing tied for 24th, six strokes off the lead.
"It only took me about eight months to get to number one in the world," Woods said. "To get to 129 cuts in a row or whatever it's at now ...it's taken more than just eight months. That's why I'm more proud of that."
Woods needs to finish ahead of Singh to keep his ranking and also hope that South African Els does not play well enough to pass both of them.
"If you win tournaments, it'll take care of itself," Woods said of the ranking.
"It always has. Greg (Norman) was number one in the world for a long period of time and he was winning two to four a year for every year, and I did the same thing, I did five plus for five straight years, and now Vijay has won five times this year.
"That's how you do it. You don't get to number one in the world by finishing top 10. You have to win."