(Reuters) - With the Ryder Cup just over a month away, the teams are shaping up, with this week's Barclays tournament at Bethpage determining the last three automatic spots on a United States team desperate to end Europe's recent domination.

U.S. Open champion Dustin Johnson, Jordan Spieth, Phil Mickelson, PGA Championship winner Jimmy Walker and Ryder rookie Brooks Koepka are set for the trip to Hazeltine outside Minneapolis for the biennial matches starting on Sept. 30.

Eight players automatically qualify from the U.S. points list, creating a scramble for the last three on offer from candidates such as (number six) Brandt Snedeker, Zach Johnson, Patrick Reed, Bubba Watson, Olympic bronze medallist Matt Kuchar and Rickie Fowler.

U.S. captain Davis Love III will add four other players as captain's picks to a team who have lost the last three match play competitions to Europe.

Europe have already assembled their first nine in a group featuring Rory McIlroy, British Open winner Henrik Stenson, Olympic champion Justin Rose and cup veteran Sergio Garcia, plus five rookies including Masters winner Danny Willett.

Joining Willett on the Europe side are fellow British first-timers Chris Wood, Andy Sullivan and Matthew Fitzpatrick, and Spain's Rafael Cabrera-Bello.

Europe captain Darren Clarke has three wild-card choices to announce on Aug. 30 and said at last month's PGA Championship he would probably seek to balance his rookie contingent with players with Ryder Cup experience.

Clarke indicated that his frequent Ryder Cup playing partner Lee Westwood, who narrowly missed qualifying, was a likely pick when he is expected to name his selections, also on Aug. 30.

"He's been my partner in many, many Ryder Cups," Clarke said at Baltusrol.

"I know what Lee Westwood brings to the table, and I know what he brings to the back room, and there's not many guys you'd prefer to go shoulder to shoulder with."

Another strong candidate for Clarke's consideration is likely to be Germany's Martin Kaymer, twice a major winner, who made the clinching putt in the 2012 Ryder Cup at Medinah, along with in-form Thomas Pieters of Belgium and Scotsman Russell Knox.

(Reporting by Larry Fine in New York; Editing by Clare Fallon)