The conversations are said to have been exploratory, and no signing is imminent, according to the source.
Burress hasn't been able to find a landing spot after catching 45 passes for 612 yards and eight touchdowns last season with the New York Jets.
The Cowboys have experienced a litany of wide receiver issues throughout the offseason. Dez Bryant was arrested in July on a misdemeanor domestic violence charge, and owner Jerry Jones said the third-year pro is "very vulnerable." Miles Austin has been sidelined with a strained hamstring, and the Cowboys are still looking for a No. 3 wide receiver to replace Laurent Robinson, who signed with the Jacksonville Jaguars in the offseason.