The Sun says the FAW see the legendary Manchester United winger as the man to raise the fortunes of the national side with John Toshack set to quit today.
And they are exploring the possibility of bringing in Giggs as assistant to Under-21 boss Bryan Flynn - both in caretaker roles - for next month's Euro qualifiers against Bulgaria and Switzerland.
Giggs, 36, could hang up his boots at the end of the season and the FAW's latest plan would see him take over then.
An FAW source said: "It is no secret that the fans want Ryan and he would certainly lift the players.
"We are exploring the options and there is no need for us to rush into an appointment."