The highly-rated 17-year-old midfielder has attracted the attention of a host of Premier League clubs, with the FA Cup winners reportedly leading the way.
However, Parkinson told the News Shopper: "There is no truth in the Chelsea story that I know of and it is just paper talk."
Meanwhile, the Addicks squad returned for the start of pre-season training on Thursday and Parkinson was pleased with the fitness levels of his players.
He added: "It was very good and the players were excellent. We had them monitored over the summer and they came in earlier this month for some tests, so we already knew they had been looking after themselves."