PITTSFORD, N.Y. — Tiger Woods and Phil Mickelson are again atop golf’s hierarchy, renewing interest in their rivalry for this week’s PGA Championship, where Woods is seeking to end a five-year major drought and Mickelson is looking for his second straight win in a Grand Slam event.

Woods, No. 1 in the Official World Golf Ranking, enters this week fresh off his eighth career victory at the Bridgestone Invitational. Mickelson, No. 2, is three weeks removed from his back-to-back titles at the British Open and the Scottish Open. Ten years ago when the PGA Championship was held at Oak Hill, Woods and Mickelson also entered the tournament as favorites.

While a lot has changed between golf’s two biggest names since the event was last played at the Rochester course, the potential for a showdown still looms large when action begins Thursday. Mickelson, with five major titles to Woods’s 14, said he is ready for it.

“I’m as motivated as ever to compete and to play and get the best golf out of me to hopefully play against Tiger when he’s playing his best,” Mickelson, 43, said in a press conference Tuesday. “That would ultimately be the goal; if I can play as well as I can at the same time he’s doing the same, I would love that opportunity.”

Mickelson’s win at the British Open on July 21 moved him past Rory McIlroy, Justin Rose and Adam Scott from No. 5 in the ranking to No. 2. He and Woods hadn’t held the top two world- ranking spots since Sept. 26, 2010.

Woods said he’s worrying less about Mickelson and more about the winner’s Wanamaker Trophy.

“Phil and I have certainly battled in a few majors and a few tournaments here and there,” Woods said. “Not as much as people think.”

Woods, 37, is a 4-1 favorite to win this week, according to LVH Super Book assistant manager Jeff Sherman. Mickelson is next at 15-1, tied with Masters Tournament winner Adam Scott of Australia.

Woods had won four times heading into the 2003 PGA, where he finished 39th, and would later add his fifth win of the season at the American Express Championship. He ended that year without a major for only the second time in his first seven full seasons on the U.S. PGA Tour. He has ended each of the past four seasons without a win in a Grand Slam event, with his last major title at the 2008 U.S. Open in Torrey Pines near San Diego.

The drought appears to have forced Woods to adjust his high standards. Even without a major win on his list of 2013 accomplishments, Woods said at a news conference today that it has been a “great year” for him, an assertion he had long reserved only for seasons that included a major trophy.

“Look at the quality of tournaments I’ve won,” Woods said, referring to victories in two World Golf Championship events and the Players championship, tournaments that attract the world’s best golfers. “That’s pretty good.”

In 2007, when he was winless in the first three majors, Woods said in his pre-PGA press conference that his season had been “pretty good, but not great” without a major. At that point, he had won four events, including two World Golf Championships, and won the year’s major finale.

Individual records aside, one thing remains certain when it comes to Woods and Mickelson.

“Every tournament, they are a threat to win,” said 31- year-old American Hunter Mahan, who was paired with Mickelson in the final group at this year’s British Open. “Especially right now. It’s pretty impressive to see that their longevity is continuing.”

Mahan cautioned against defining the duo as true rivals in golf, a sport where players compete more against the course than other players.

“I think people want them to be together for a rivalry’s sake,” he said. “It’s hard to just have two guys battle it out each week. Golf is not like that.”

Their differing personalities help make the matchup more intriguing, even to Mahan.

“They are just so different in every way,” he said. “I don’t know of a common thing other than they love to compete when they play golf. How they go about it is just so different, but they both get it done.”

Following a win at a tour event with a victory in a major the next week hasn’t been easy for Woods. In 17 previous opportunities, he has won four majors after winning a U.S. tour event, most recently at the 2007 PGA.

The statistic wasn’t overlooked by Mickelson, who took the chance to point out that he is playing as well, if not better, than Woods coming into this week.

“Having Tiger win last week is great,” he said. “Because I can’t remember the last time somebody won the week before a major and then went on and won.”

That was an unspoken reference to his win at the Scottish Open the week before his British Open victory last month.

“It’s great for the game,” Mickelson said.

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