Wales have played only once at the 74,500-capacity rugby citadel since 2011 - a high-profile friendly against former European and world champions Spain in October 2018.
The 33,280-capacity Cardiff City Stadium has proved a popular and successful base for the men's national team over the last decade, with Wales having qualified for the European Championship finals in 2016 and 2020.
"We have an agreement with Cardiff City Stadium and everyone really likes going there," Football Association of Wales chief executive Noel Mooney told the PA news agency.
"But we'll actually speak to the Welsh Rugby Union late next week. Absolutely we're in discussions with them.
"Just to make sure that if a match comes that, for whatever reason, Cardiff City Stadium is not available.
"Or if there's a real big feeling that people want to go to the Principality Stadium."
From 2000 to 2009, the then-named Millennium Stadium was the almost-permanent home of Welsh football.
Wales packed out the stadium in the early years when beating the likes of Germany and Italy and boasted the largest attendances in the whole of Europe.
But the crowds dwindled as the team struggled and the far smaller Cardiff City Stadium was seen as a better fit for the national team.
Next year, Wales face a potential World Cup play-off game in March as well glamorous fixtures in June and September after being promoted to the top tier of the Nations League.
The draw for the 2022-23 Nations League will be made in December and Wales could attract large crowds if paired with the likes of England, world champions France and European champions Italy.
On the possibility of switching games to the Principality Stadium, Mooney added: "It's something we could well do. Why not?"
Mooney joined the FAW in July after spending 10 years at UEFA, most recently as the European football governing body's head of strategic development.
The Irishman says he has spoken "briefly" to Wales manager Ryan Giggs, who has been on leave from his post since November 2020.
Giggs faces charges of assaulting two women and controlling or coercive behaviour and is due to stand trial in January. The former Manchester United and Wales star denies the charges.
Mooney said: "I spoke to Ryan briefly when I joined. He's on a contract with us and we had a pleasant phone call.
"We're just waiting. It's in a process. We're waiting to see how that pans out."
Robert Page, who was a member of Giggs' backroom staff, has been in charge for the last 11 months.
Page led Wales to the last 16 of the delayed 2020 European Championship in the summer and has overseen the 2022 World Cup qualifying campaign.