The Sun says he will step aside for Wales' next three games after being arrested on suspicion of assaulting his girlfriend. The Welshman has denied the allegations.
Wales are due to play the USA in a friendly in Swansea next Thursday.
They then have two Nations League matches, both in Cardiff, against Ireland and Finland.
Giggs will not take charge of the side for those fixtures.
The Welsh legend is assisted by Albert Stuivenberg and Osian Roberts.