Bernhard Langer, Ian Woosnam and Sandy Lyle are considered the candidates to captain the European team for the 2004 event at Oakland Hills in Michigan.
Woosnam has said he would like Langer to get the 2004 captaincy and then take over himself for the 2006 event in Ireland.
Montgomerie said the decision should be made privately.
''It seems to be played out too publicly and I don't feel that's right, personally,'' the Scottish Ryder Cupper said.
Montgomerie cited the private selection of Hal Sutton as captain of the American team.
''Who knows what happened behind the scenes, but what happened behind the scenes there is happening here in front of the camera,'' he said.
''I don't want Bernhard or Ian or Sandy to feel they've lost out. Then what happens? Do they bid again and give themselves the opportunity to lose again? What happens to the losers?''
Asked if he expected to have a chance to captain the Europeans in the future, Montgomerie replied: ''Given the opportunity I'd be honored to do it anywhere and any time.''
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