Tykes boss Simon Davey has made no secret of his interest in former Burnley frontman Gray, but Parkinson warned he will not be sold on the cheap.
"Barnsley have been talking to us all summer [about Gray], but at the moment the deal just doesn't add up and it's nowhere near the valuation we've got of the player."
"Andy played for a lot of last season with a stress fracture. He's now fit and he's trained well. He's available for selection and he could be a big player for us this year."
The Addicks boss also warned League One rivals Gillingham that he would only be willing to let Dickson leave in a swap deal involving an unnamed Gills striker.
"Gillingham have been talking to us about Chris all summer, and we keep telling them he's not going there. We've now said to them that we'll let him go there if they give us one of their strikers in exchange. I won't give you the name of him, but you might be able to guess. If that deal doesn't happen, then Chris isn't going to go there."