Clarke was handed the reins after McGinley had engineered a European success at Gleneagles in 2014 but was powerless to stop the USA easing to victory by 17 points to 11 at Hazeltine.
It was the first time the Americans had lifted the trophy since 2008 and thoughts have already turned to Le Golf National in France for Europe's attempt to win back the spoils.
Two names have been mentioned as possible captains, with Ireland's Padraig Harrington and Thomas Bjorn of Denmark thought to be top of the list.
And, according to McGinley, the public will not have to wait too long to find out who has got the nod.
"We’ll be appointing a new skipper probably this side of Christmas," McGinley told Reuters. "We are very disappointed to have lost the Ryder Cup. It hurts to lose.
"The event goes from strength to strength, this time it didn’t go our way but we’ll re-galvanise and come at the Americans again."