The Palm Beach Post, quoting sources, said Williams tested positive for marijuana on Dec. 10, 2003. The sources said he is appealing the fine and was seen at NFL headquarters in New York April 16, the date of the appeal.
The Miami Herald said Williams is awaiting an arbitrator's decision.
"I'm in good standing with the NFL and the Dolphins," Williams said. "There is not a story here. I guess that's how rumors get started. I will be at training camp on Tuesday."
Officials of the NFL and the Dolphins had no comment.
The 26-year-old Williams first tested positive for marijuana shortly after arriving in Miami in May 2002 from New Orleans, the Post said.
Williams has gained 6,354 yards and scored 41 touchdowns in his five-year NFL career.
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