Only the top 64 qualify for Arizona, but Ernie Els has not put the event on his schedule and if Montgomerie stays where he is for two more weeks that would mean an opening day clash with world number one Woods.

The 44-year-old Scot’s love of match play is based on the fact that he has never lost in eight Ryder Cup singles – but he has never faced Woods and has never won a tournament in which the American has been playing.

Martin Kaymer’s victory in the Middle East has swept him all the way from 76th to 34th, making the 23-year-old German the only player in the world’s top 50 under the age of 25.

Kaymer can look forward to making his world championship debut in Tucson and will play the first major of his life at the Masters in April if he is still in the top 50 the week before the event.

Lee Westwood is back in the top 20 after finishing joint runner-up with Henrik Stenson.

Latest leading positions on world rankings:

1 Tiger Woods 18.44,

2 Phil Mickelson 8.43,

3 Steve Stricker 6.82,

4 Jim Furyk 6.36,

5 Ernie Els 6.18,

6 Justin Rose 6.00,

7 KJ Choi 5.81,

8 Adam Scott 5.49,

9 Rory Sabbatini 5.36,

10 Padraig Harrington 5.27,

11 Vijay Singh 4.98,

12 Sergio Garcia 4.70,

13 Geoff Ogilvy 4.41,

14 Angel Cabrera 4.20,

15 Henrik Stenson 4.17,

16 Zach Johnson 3.87,

17 Aaron Baddeley 3.79,

18 Luke Donald 3.71,

19 Trevor Immelman 3.55,

20 Lee Westwood.

Other leading Europeans:

21 Ian Poulter,

22 Niclas Fasth,

23 Paul Casey,

34 Martin Kaymer,

39 Miguel Angel Jimenez,

40 Robert Karlsson,

48 Soren Hansen,

50 Nick Dougherty,

51 Anders Hansen,

55 Peter Hanson,

57 Bradley Dredge,

61 Daniel Chopra,

65 Colin Montgomerie,

66 Mikko Ilonen,

68 Carl Pettersson,

70 Simon Dyson,

75 Soren Kjeldsen,

78 Steve Webster,

80 Bernhard Langer,

83 Jose Maria Olazabal,

84 Fredrik Jacobson,

88 Ross Fisher,

93 Gonzalo Fernandez-Castano,

97 Raphael Jacquelin.