Speed was appointed as John Toshack's successor in the Wales hotseat last week and he is now in the process of forming his back-room team.
Giggs was the early favourite for the top job but, with six months still to go on his current United contract, it was a no-go.
However, the 37-year-old, holder of a record 11 Premier League titles and 64 Wales caps, could be tempted to take a smaller role.
Speed told BBC Sport: "It would be great to get him involved in some respect. I spoke to him last week and we'll have to wait and see."
Giggs, who is taking his coaching badges, succeeded Speed as Wales captain in 2004 before retiring from the international game three years later in order to prolong his club career.