The committee that chooses the captain will make the decision Wednesday in Dubai on the eve of the Dubai Desert Classic. Two-time major champion Sandy Lyle and 2006 captain Ian Woosnam are also being considered for the job.
If it's Montgomerie or Olazabal, Europe will have its youngest captain ever when the tournament is held in September 2010 at Celtic Manor. Montgomerie will be 47 when the competition starts, and Olazabal will be 44.
The United States has already chosen Corey Pavin as its captain. He will be two months short of his 51st birthday at the time.
Montgomerie, a Scotsman who has earned 23-1/2 points in his Ryder Cup career, is the second most successful European player behind Nick Faldo with a record of 20 wins, 9 losses and 7 halves.
'Having played in eight Ryder Cups, it doesn't really affect what or how I would help the European cause one way or another,' Montgomerie said this month. 'I would like to help the European cause in any way, shape or form. It would be an honor to be to be selected.'
Olazabal was Faldo's vice captain last year when Europe lost the Ryder Cup by 16-1/2 to 11-1/2 at Valhalla. Olazabal's former playing partnership with fellow Spaniard Seve Ballesteros is regarded as one of the most successful pairings in Ryder Cup history.
Both Montgomerie and Olazabal had earlier expressed the desire to make the 2010 Ryder Cup team as players, with Montgomerie hoping to get the captaincy in 2014 when the event is played in Gleneagles, Scotland.
Third-ranked Padraig Harrington, who has won three of the last six major titles, believes Montgomerie would be a good choice for Europe.
'I'd be all for Monty. I think we need to put our absolute best foot forward at the time and I believe he is the man for the job,' the Irishman said. 'I'd certainly like to see him as captain and I think that will give us our best chance of winning in Wales.'
The committee may announce two captains ' possibly Montgomerie for 2010 and Olazabal for 2012, when the Ryder Cup shifts back to the United States.
'I have read all the arguments saying Monty would be great in Europe and then Olazabal in the States with his rapport with the fans and the people, but I don't care,' two-time Ryder Cup winner Paul Casey of England said. 'I just want to be on the team and play for one of them.'