Dewsbury-Hall, while an England U21 international, also qualifies for Ireland and McAteer says the FAI must make an approach.
McAteer told the Liverpool Echo: "It's not rocket science, just good old-fashioned man management. You've got to be a little bit more creative with your managers and what your aspirations are.
"Dewsbury-Hall, let's use him for a minute as an example, it's unlikely he's going to play for England, but does he want to go and play for Ireland? When they are getting battered by the media and getting battered against Armenia?
"He's not going to want to do that. But if you get a manager who comes in and entices him in and protects them and looks after them and gets the media back on side and gets a bit of enthusiasm with the fans, he just might accept the offer.
"You'll find players will start reacting to that, and they'll say, Yeah, I'll come play for you. I'm not going to play for Spain. I'm not going to play for Italy. I'm not going to play for Germany.
"I'm not going to play for England or Scotland; I'll come and play for Ireland. I know there's that patriotism that goes into international football, of course, it's there.
"I wanted to play for Ireland. When I saw Jack come into Bolton, I didn't know whether he was going to ask me or not, but I wanted to play for Ireland. I didn't want to play for England. My granddad was from Northern Ireland, County Down.
"England was never really an option and when Jack said; 'Do you want to play'? I said, Yeah. I rang Jimmy Armfield and said, listen; 'I'm going to play for Ireland'. I wanted to do it. So, yeah, you've got to be creative.
"It's not really rocket science. If things don't work out with the current manager, and I don't love to do this, then my choice would be John O'Shea... If John O'Shea rings Dewsbury-Hall up and says; 'Do you want to come and play for Ireland'? I dare say he'd accept. That's a good start."