The Browns plan to release Gordon on Monday unless they find a trade partner first. Lynch said the 49ers are doing their due diligence on the receiver, who has an extensive history of problems off the field.
Gordon showed up late to the Browns' facility Saturday morning with a hamstring injury, which he reportedly sustained during a promotional event.
The 27-year-old also reportedly has his eye on San Francisco and the Dallas Cowboys as preferred landing spots. The 49ers have a major need at receiver, especially with Marquise Goodwin nursing an ailing quad.
Gordon caught just one pass for Cleveland in Week 1, although it was a game-tying touchdown late in the fourth quarter against the Pittsburgh Steelers.