The 44-year-old is now working as a TV pundit after leaving his position as assistant to Louis van Gaal at United when the Dutchman departed Old Trafford at the end of the 2016 season.
Coleman left the Welsh team after failing to qualify for this summer's World Cup in Russian Federation and has since joined Sunderland.
Giggs, who played for Wales 64 times, has made no secret of his desire to succeed Chris Coleman as national team manager, which previous year he described as the ideal job.
The 38-year-old, who represented Wales 78 times but has no managerial experience, is working in Cardiff's academy.
The interviews took place on Thursday (Jan 11), overseen by Jonathan Ford, the FAW chief executive, and it is anticipated that a decision will be made quickly, with Giggs now the front runner. A FAW press spokesman did not immediately respond to a Reuters request for comment on Friday.
Grace hunting more SA golf glory
Branden Grace scored three eagles in a seven-under-par 65 for a share of the lead after the South African Open's first round. I was quite aggressive with the three-wood and I managed to knock it about 25 feet and managed to roll in the putt.
"It would be a great job".
Manchester United legend and Welshman Ryan Giggs has reportedly been interviewed for his country's job, possibly starting his career in management on the worldwide stage.
Giggs and Bellamy were interviewed despite never having held full-time managerial roles, though former Manchester United winger Giggs was the caretaker boss at Old Trafford in the wake of David Moyes' departure back in 2014.
Bowen has been linked with management positions in the past but has remained loyal to Hughes - and left with him when Hughes was sacked following last weekend's embarrassing FA Cup defeat at League Two Coventry.