The 17-year-old has been a bright spark in an otherwise miserable season for the relegated Addicks, breaking into the first team and scoring four goals along the way.
That has sparked speculation of a move to the Premier League but Parkinson insists no club has yet made an offer for the midfielder.
"I haven't had one call about Jonjo," Parkinson told the club's official website. "But the supporters expect this kind of thing. They know he's going to be linked with other clubs in the papers. When the Premier League season finishes, they need to fill their pages and they do so with speculation.
"We'd like to keep him and build a team around him. We all know he's a good player and he wants to stay. He's a Charlton boy and he wants to get this club promoted but obviously you can never say never.
"I can't make any promises because of where we are financially, but he hasn't shown any signs of his head being turned and he hasn't let it (transfer speculation) affect him."