The extension comes weeks after the 24-year-old Wade was named the Most Valuable Player of the NBA Finals.
He had per game averages of 34.7 points and 7.8 rebounds, helping the Heat beat the Dallas Mavericks in six games to win their first NBA title in June.
Miami became only the third team in league history to come back from a 2-0 deficit to win the title. His agent, Henry Thomas, confirmed the offer to the South Florida Sun-Sentinel, and said he expects the deal to get done quickly.
The offer was made shortly after Saturday's signing period for teams negotiating deals with their own free agents.
"We're on the same page," Thomas told the newspaper.
Wade was due to make $3.8 million in the 2006-07 season, the final year of his rookie deal in 2003.
Aaron Carter is still in love with Hilary Duff
Ray Liotta sues skin care company over use of likeness