Sergio Garcia, Ian Poulter and Lee Westwood, who have played 28 Ryder Cups between them and are now with the LIV Series, are ineligible for this year's edition of the biennial competition after resigning from the DP World Tour in May.
However, American players who joined the LIV circuit can still qualify for the U.S. team given they are members of the PGA of America.
"To ignore LIV because of politics when the U.S. have those players in their side doesn't make any sense," former Europe vice-captain McDowell, who plays for the Saudi-backed circuit, told the BBC. "It makes Europe's tour look foolish.
"I hope that if one of the European players at LIV puts in a summer deserving of a spot on the Ryder Cup side that the landscape would be available for that to happen."
The PGA Tour, DP World Tour and rival LIV circuit, which had been involved in a bitter fight that split the sport, announced an agreement in early June to merge and form a unified commercial entity.
Northern Ireland's McDowell, who was on the winning team in three of his four Ryder Cup appearances, also called for Europe's all-time record points scorer Garcia to be reinstated.
"I think Sergio Garcia is probably the lead guy right now and the European team room would be better with a Sergio Garcia in it," McDowell said.
"I read the stuff with him and Rory McIlroy (resolving their differences) and I'm super happy that those guys have moved on from stuff that shouldn't have come between them - politics and business.
"I'd love to see them walking down a fairway in Rome, winning a foursomes match together. I think that's what every European Ryder Cup fan wants."
The Ryder Cup runs from September 29 to October 1 at the Marco Simone Golf and Country Club near Rome.
