Other Ryder Cup players include the England trio of Ross Fisher, Oliver Wilson and David Howell, Frenchman Thomas Levet and Welshman Phil Price.
A field of 96 players will take to the Surrey course with the top 12 assured entry into the British Open starting on July 19 at Royal Lytham and St. Annes.
Montgomerie played every British Open from 1990 to 2010 before missing out on qualifying last year.
The Scot, who turns 49 on Saturday, recently tried to qualify for the U.S. Open but was unsuccessful.
McGinley has missed out on qualifying for the past two years.
Also competing Monday will be 45-year old American Billy Mayfair, who last contested a major in the 2009 British Open, finishing 52nd.
Among the reserves seeking entry into the qualifier is Sweden’s Niclas Fasth, who was runner-up in the 2001 British Open, the last time it was staged at Royal Lytham and St. Annes.