The European Tour is set to announce a replacement for the victorious Jose Maria Olazabal early next year with Darren Clarke firm favourite to lead the defence of the trophy at Gleneagles in Scotland.
Clarke went public in the week after Europe's stunning one-point success over the United States at Medinah, stating he would embrace the 2014 captaincy with both arms if offered the position.
The former Open champion, through a European Tour directive, is now refusing to discuss the issue further but Donald and McDowell have singled out McGinley as their choice.
"From a personal point of view, and probably because I have spoken a little bit more to Paul McGinley, I find him a little bit more outgoing with me," Donald said on the eve of the BMW Masters in Shanghai.
"Paul always seems very up for the challenge. But then I do believe that if he doesn't get it this year, he probably won't get it at all. Whereas, I feel like Darren will have other opportunities.
"So I would support McGinley as he's been very diligent, very enthusiastic and whenever I have been around him I have enjoyed it.
"He just has a really good team vibe. He seems to think about the small things. That's just what I've noticed."
McDowell has now played in the past three Ryder Cups, including two in the United States, and he suggested fellow Northern Irishman Clarke might be more suited to captain the team in 2016 at Hazeltine in Minnesota.
"Both Paul and Darren would be great captains in their own right but then Paul has kind of forged a little niche for himself given the way he has conducted himself in the Seve Trophy and the Ryder Cup vice captaincy roles," said McDowell.
"He's a scholar of the game and a strategist and would probably be technically, if that's the right word, a good captain.
"Darren would emotionally be a great captain and a great motivator, and also with that big personality he possesses.
"Darren's credentials may be better but I think he would make for a great captain in America as they love him over there. His personality suits America and they see him as the cigar-smoking, Guinness-drinking, nice guy that he is.
"So, Darren would go down well in the States whereas Paul also has all those traits that would make for a great Ryder Cup captain."
McDowell said careful thought needed to be given to what factors were considered when deciding who should lead the European team.
"If it should boil down to pure playing credentials, of course, Darren would win hands down as the next captain," said McDowell.
"However, that opens a can of worms on the Ryder Cup captaincy debate because are we looking for a captain who has the right playing credentials or are we looking at Ryder Cup captains who will be great captains?
"You've got to look at what makes a great captain and it's personally being able to relate to 12 very individual players in a team.
"It's to do also with people skills and being able to possess organisational skills as well as leadership qualities as they all go into making for a great Ryder Cup captain.
"But then, given Ireland has never had a Ryder Cup captain, someone is going to be disappointed, especially if it's not Paul, as he will be disappointed as he might not get another shot.
"Gleneagles is certainly his most legitimate shot because if Darren is handed the role for 2016, you're then starting to look at Lee Westwood and Padraig Harrington being captain."
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