Chudzinski addressed a report from ESPN NFL Insider Adam Schefter that the San Francisco 49ers had talked with the Browns about acquiring Gordon.
"I will say we're not shopping Josh and have no plans to trade Josh," Chudzinski said.
This week marked the second time reports circulated about Gordon being on the market.
The first came just before the Browns played the Minnesota Vikings in Week 3, Gordon's first game back from a two-game suspension.
At that time, Gordon said he wanted to stay with the Browns. Presumably, that remains true, though Gordon was not in the locker room during the portion open to the media.
In three games, Gordon has 18 catches for 303 yards and two touchdowns. He is the Browns' best playmaker, with all seven of the touchdown receptions in his career 20 yards or longer.
"Within here, any kind of distraction like that has been a non-issue," quarterback Brandon Weeden said. "Those things are out of our control as players. I'm sure he's been asked the question and he's worried about playing this week."