McDowell reached the last 16 in Arizona with a 4&2 win over Ross Fisher
Graeme McDowell will overtake Tiger Woods in the world rankings on Sunday and could even climb to his highest position of third in the world.
US Open winner McDowell or Englishman Luke Donald could be world number three after they both reached the last 16 of the WGC Match Play in Arizona.
"I'm perhaps a better golfer than Tiger in the last 12 months but he's the greatest player," said McDowell.
"It would be nice to slip past him for a little while."
Northern Ireland's McDowell beat Ross Fisher in Arizona to set up a last-16 tie with Korea's YE Yang.
If someone told me at some point in my career I would be number three in the world I'd be proud of that fact
McDowell knows that should Donald win the tournament, he will have to be among the semi-finalists to take the world number three spot.
"If someone told me at some point in my career I would be number three in the world I'd be proud of that fact," added McDowell.
The Portrush man started last year ranked 50 in the world but has swiftly moved up the rankings during the last 12 months.
He became the first European for 40 years to win the US Open when he triumphed at Pebble Beach in June and his five-foot putt on the 17th green at Celtic Manor helped Europe beat the United States in the Ryder Cup.
Martin Kaymer, meanwhile, has a chance of replacing Lee Westwood as world number one after Westwood's second-round defeat by American Nick Watney on Thursday.
The German, who will need to reach the final in Arizona to clinch the top spot, plays American Hunter Mahan in the last 16.