The move means Gordon's current team, the New Orleans Hornets, have three days to match the offer and retain his rights.
The New Orleans Times-Picayune reported the Suns' offer for Gordon was for four years at $58 million.
The 24-year-old guard was sidelined with a knee injury for most of the 2011-12 season after the Hornets obtained him from the Los Angeles Clippers in the deal that involved Chris Paul.
He averaged 20.6 points and 3.4 assists in just nine contests.
During his four-year career, Gordon has averaged 18.2 points and 3.3 assists in 205 games.
Earlier Wednesday, the Suns dealt veteran point guard Steve Nash to the Los Angeles Lakers in exchange for four draft picks.