Former minister of youth and sports, Aley Eddine Helal, told AFP that Warner, who is now at the heart of a corruption scandal engulfing football's world governing body, asked for the money in 2004.
"Warner was the one who approached us from FIFA. He said he could guarantee us seven votes... He asked for one million dollars for each vote," Helal claimed.
Egypt, one of African football's most dominant countries, was a candidate to host the 2010 World Cup, but it received no votes in the 2004 FIFA ballot. South Africa was chosen to host the tournament.
"We didn't pay any bribes. That was one of the reasons why we didn't get any votes," Youssef el-Dahshori, who was Egyptian Football Association president at the time, told AFP.
Signup to our newsletter and follow us on Facebook and Twitter!
Warner introduced himself in 2003 during a FIFA congress held in Qatar and proposed a meeting, Dahshori said.
"I met Warner in the UAE. He proposed to be Egypt's consultant in Latin America and Europe, since he has good connections there."
"He wanted to take seven million dollars for seven votes, and said he wouldn't take the money for himself but for developing the sport in Latin America," said Dahshori, stressing that he had refused Warner's offer.
Warner was indicted by the United States for allegedly taking a $10 million bribe to help South Africa win the race to host the 2010 World Cup, among other charges.
FIFA admitted in a statement last Tuesday that it had processed a $10 million payment from South Africa to Warner, who is one of 14 people facing charges of involvement in more than $150 million of bribes to soccer officials.