Lee Westwood shot a 3-over 75 to miss the cut at the Qatar Masters on Friday, opening the door for Martin Kaymer to replace him at the top of the rankings.
Austria's Markus Brier had a 66 to take a one-shot lead over South Africa's Darren Fichardt (68) after the second round.
Westwood, who finished 4 over, replaced Tiger Woods at the top of the rankings in October. Kaymer could advance to No. 1 with a second-place finish. He shot a 70 and is 10 shots back.
Westwood's struggles in Qatar follows a 64th-place finish in last month's European Tour event in Abu Dhabi.
"I didn't play very well," he said. "It's early season rust, I think. That's it. I'm going to go on the range the next couple of days and try to get into some kind of rhythm."
Brier is two shots ahead of defending champion Robert Karlsson (69), England's Richard Finch (69) and Denmark's Thomas Bjorn (65).
"I kept the ball in play and holed a few, two or three really long putts, and that obviously makes the difference between a good and very good round," said Brier, who has not won a tournament since the China Open in 2007.
Sixth-ranked Paul Casey also missed the cut with a 75. Casey won the tournament in Bahrain last week for his first victory in 20 months.
Kaymer has some ground to make up to attain the No. 1 ranking.
"I'm a little bit away now, but obviously if I have a good weekend, I might have a chance," he said. "I'm here to win the golf tournament, and if I take care of winning, then it will happen automatically."