Scotland will be left short-changed with just four of Europe's Ryder Cup team expected to compete in the Alfred Dunhill Links Championship, a week later, at St Andrews.
The only Medinah representatives declared for the Dunhill are the inaugural champion, Paul Lawrie, the 2003 winner Lee Westwood, the 2010 champion Martin Kaymer and Sweden's Peter Hanson.
Jose-Maria Olazabal, the Europe team captain, may also withdraw citing the short turnaround time.
Kaymer, meanwhile, heads to Chicago on Friday, breathing a huge sigh of relief after sharing fifth place in Italy with Nicolas Colsaerts.
"I had been thinking after the PGA Championship of taking six weeks off and just going straight to the Ryder Cup. So I am now pleased I did play and it's been a good and proper decision," he said. "I've gained a lot of motivation and confidence and not only for the Ryder Cup but I'm going to play the Alfred Dunhill and Portugal after Medinah."
But while Kaymer has confirmed for St Andrews, questions have been raised over a number of players who have received invitations.
Organisers have released the names of six of the 20 who will be invited to contest the event but none are Scots.Three invitations have been extended to two Americans, Pat Perez and Tom Gillis along with the Canadian Graham Deleat. Perez (135th in the world) has not played in a regular European Tour event while Gillis (138th) contested the 2008 Open in his only appearance. Deleat (153rd) has previous Dunhill form having finished down in 53rd place.
A fourth has been extended to South African Anton Haig, and for a fourth year running only because he's a friend of the sponsor while John Daly and the Dutchman Maarten Lafeber, are the others.
Scotland's Craig Lee, Alastair Forsyth and Gary Orr are all desperate for invitations but accept that it is in Dunhill's hands.
"There were 20 invitations last year but I didn't get one," said Forsyth. "I've played on the Tour 11 to 12 years, so I was disappointed, but it's entirely up to them [Dunhill]. All I can do is keep asking."
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