Edwards, who is entering the final year of his contract, said Thursday that reports of the teams' talks did not bother him.
"I didn't get excited [about the rumors]," Edwards said, according to The Cleveland Plain Dealer. "One, they were rumors and there was nothing to hold on to. And two, I felt like if I would have left Cleveland for any reason, I would have left with a bad taste in my mouth."
After a breakout 2007 season in which he had 1,289 receiving yards and 16 touchdown catches, Edwards had by most accounts a miserable '08. He was criticized for dropping balls and had 55 receptions, 25 fewer than in '07, and only three for touchdowns.
"I wanted to get back to playing good football, definitely here," Edwards said, according to The Plain Dealer. "It's a business and who knows what's going to happen next year. But for me, it was just about getting back to what I know I can do and being the player the Browns drafted in '05 and that the fans saw in '07."
In what was reported as his last discussion with the Browns, Giants general manager Jerry Reese told Cleveland he might be willing to part with a second- and a fifth-round pick. Nothing came of it and New York ended up drafting a receiver, Hakeem Nicks of North Carolina, with the 29th overall pick.
"Obviously they didn't get what they wanted, which means they felt highly of me to ask for a lot and it didn't go down that way and I'm still here," Edwards told the newspaper. "I'm happy to be here.
"There's a lot of players here that I still know, some new players. I remember [rookie receiver] Brian Robiskie at 17, having him out here when he was a ballboy and now he's one of my teammates. I think it's going to be a fun season. I'm excited to play with these guys and play in this new system and see what happens."
Edwards said he hasn't spoken to general manager George Kokinis or new coach Eric Mangini about the team's trade discussions.
"Right now I'm a Cleveland Brown and that's what I'm going to be until that day happens," Edwards said. "It won't be my decision."