US skipper Watson believes it would be a good thing for all 12 players in each team to earn an automatic place through their respective money-lists, with no wildcard selections, but Europe captain McGinley had a different view.
"If you really look at it, the purist form of Ryder Cup would be no captain's picks and 12 players who qualify," Watson told a joint news conference in Scotland to mark the one-year countdown to next year's biennial team event.
"I reduced my picks this year from four to three and was thinking actually two because I wanted the players who are playing to get on the team, to have that as a goal.
"If they get there then they have earned something very, very special and maybe we should go back to no picks."
As soon as he finished his sentence, the 64-year-old Watson turned to McGinley to enquire, "What do you think about that, Paul?".
McGinley, however, cited the amount of top European golfers who ply their livings on the U.S. Tour as a reason for keeping the wildcard system in place.
"It's a different dynamic on the European side when we have so many players playing on the PGA Tour so let's defer that one, thank you," said the Irishman with a typically broad grin.
Watson and McGinley were involved in a hectic schedule of events on Monday and Tuesday and both men said they had enjoyed spending time in one another's company.
"Anybody who knows Tom Watson knows how much of a competitor he is and he's not going to let his guard down at any stage," said the Irishman. "So I didn't expect anything and that's the way it's been."
"Come on, Paul," interjected the American as laughter broke out around the room.
"We have spent a lot of time together over the last two days and it's been fun getting to know Tom better," McGinley added.
Eight-times major winner Watson's mood was somewhat less jovial when the 64-year-old was quizzed about being the oldest captain in the history of the event.
"Age is not an issue at all because the players that will be on my team know I've been a player at the Ryder Cup," said the American.
"They know I've been a captain (in 1993) and they know that I know that they know ... and that's all that matters."
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