The Daily Mail says Toshack will resign as Wales boss within 48 hours and has already recommended Giggs as his replacement.
Toshack contacted the FAW officials and told them he had been upset by the level of criticism.
He said that he would stay on while they found a replacement. He is understood to have been asked his opinion on his successor and has suggested Giggs.
The winger retired from international football three years ago and would be exactly the kind of stellar name that could help reinvigorate football in the Principality.
The FAW have just appointed a new chief executive, Jonathan Ford, who is keen to make his mark and the mere suggestion of Giggs's possible arrival will certainly whet the appetite in their Cardiff headquarters.