Gordon has been linked with a move to the San Francisco 49ers recently after reports surfaced suggesting that last season's Super Bowl runners-up were interested in the 22-year-old.
However, Weeden insists that none of the players, including Gordon, have given the rumours much thought as they prepare for their next match.
"Within here, any kind of distraction like that has been a non-issue. 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," he told reporters.
Cleveland face the Detroit Lions on Sunday as they look to extend their winning streak to four matches.