Bowen, currently assistant manager at Fulham, put the name of Manchester United winger Giggs forward after Sky Sports News revealed that current Wales manager John Toshack would be prepared to leave his post as soon as a successor can be found.
Toshack - who has steered the nation to 21 wins in 53 games - said that he would be back in charge for Wales' next game after Friday's 1-0 defeat to Montenegro in a Euro 2012 qualifier.
But the Football Association of Wales is expected to make a statement to clarify his position this week.
"If John feels he has taken them as far as he can and he's maybe lost a bit of enthusiasm for the job, then it's crying out for a fresh face to come in," Bowen told Sky Sports News.
"You usually find across the board when a new man comes with a group of players that you tend to have an instant impact, if you like. It's something that Wales really need, possibly going into the next game against Switzerland."
Giggs, who has previously said that he would consider a coaching career once his playing days are over, agreed a new one-year deal at Manchester United in February 2009 that will keep him at Old Trafford until June 2010.
And Bowen said: "I've seen the names in the frame (for the Wales job) and Ryan's got a mention and Chris Coleman. Those are the two that stick out for me.
"As far as Ryan's situation goes, if they want to offer him the job it will depend on his decision and no doubt he will take advice from Sir Alex on that as well.
"Whether he can combine the two, who knows? Mark Hughes combined the two for a short time at the end of his playing days when he was at Blackburn Rovers.
"Time will tell if Ryan can do it and would want to do it. It would be a steep learning curve. He'd have to deal with the pressure of trying to get results in international football. But perhaps the expectation isn't as high as maybe it once was.
"I've no doubt that if they want to go along those lines then Ryan will have the best shoulder to lean on and the best person to go to for advice in Sir Alex (Ferguson).
"Sir Alex might be hearing this news breaking and he might be thinking the last thing he wants is Ryan having to concentrate on two things.
"But there are other candidates out there - Chris Coleman, Dean Saunders and Brian Flynn who has done a fantastic job with the Under 21s.
"From Chris Coleman's point of view, he's available, he's out of the game at the moment and he's probably desperate to step in and take the reins and that wouldn't be a bad decision either from my point of view."