Newsday, citing an anonymous source, reported that the Jets plan to place a contract tender on Edwards, a restricted free agent in March, that would require a team to give New York first- and third-round picks if it signs him.
"I hadn't heard anything about it, but if that's something they're definitely doing, I'm excited," Edwards said. "I love playing here and I love the atmosphere around here. It's a family atmosphere that's centered around winning. If that's what's going on, I would be extremely happy and proud to be a Jet for years to come."
Edwards, a former first-round pick out of Michigan in 2005, was traded from Cleveland to New York in October after four-plus seasons with the Browns.
"I've seen one side and this is another side, and I don't want to see another side," he said. "I think this is my side right here."
Edwards has four catches for 56 yards in two postseason games with the Jets, who play at Indianapolis on Sunday for the AFC championship. He finished the regular season with 35 receptions for 541 yards and four scores with New York.
"It's crazy," he said. "I never would've thought I would be in this situation. So, to be here is just a blessing and I'm excited. I'm trying to keep my cool, but we're one win from playing in the big dance."
It's been a hectic year for Edwards, who has been highly criticized for dropping too many passes during his career. He was accused of punching a friend of NBA star LeBron James on Oct. 5, was traded to the Jets two days later and then pleaded not guilty to misdemeanor assault in November.
Edwards was placed on probation last Tuesday after pleading no contest to misdemeanor aggravated disorderly conduct, and could face discipline from the NFL after the season.
He said he is focused only on football now, and is excited about the prospect of playing several years with Mark Sanchez after going through various quarterbacks in Cleveland.
"That's definitely another thing for me, just stability, period," Edwards said. "One, having a guy like Mark who's progressing well and has been taking some tremendous strides over the last four weeks. Also, just having the team we have in place, our team is consistent. ... There's a lot of consistency and a lot of stability and that's how you win at this level."