Speed was unveiled as Wales' latest national team boss after penning a three-and-a-half-year deal on Tuesday and has made it clear that the door remains firmly open for 'retired' stars, who include Fulham's Simon Davies and Danny Gabbidon of West Ham United as well as Giggs and Savage.
The quartet quit international football under previous chief John Toshack, but Speed admits he is hopeful of convincing them to reconsider.
"I am sure I will be ringing around. There are a couple who have already rung me to be honest. Sav rang me.
"I'm not sure about Ryan yet, but who wouldn't want him in a team? I'm sure others will be in touch."
Savage, who currently captains Championship outfit Derby County, has not made an appearance since falling out with Toshack in 2005, while Giggs announced his retirement three years ago.
Speed, meanwhile, realises that his squad is short of vital experience to supplement the young talents of Gareth Bale, Aaron Ramsey and Joe Allen.
The former Sheffield United manager is Wales' record cap holder for an outfield player with 85, and wants players to relish the opportunity of playing for their country.
"It's up to me to impress to the players how much enjoyment they can get from playing for Wales. What we haven't done over the last four or five years is actually beat anyone of stature. We must get back to that."
By Greg Lea
