Welker is currently playing under the franchise tag with a $9.5 million tender, and the sides only have until July 16 to reach a long-term deal.
The Patriots recently signed Rob Gronkowski to a six-year, $54 million contract which makes him the highest-paid tight end in NFL history. Welker, 31, has yet to be given the same security despite catching 122 passes for 1,569 yards and nine touchdowns last season.
The wide receiver said he harbors no jealousy for Gronkowski.
"I'm always pulling for the players," Welker said, according to ESPNBoston.com, "especially a guy like Gronk, who does such a great job for us and works hard and deserves every bit of that contract."