After missing out on last Saturday's home win over Crewe Alexandra, Hanson was expected to be a strong contender to play at Oakwell in front of the Sky Sports cameras but now Parkinson has conceded that the striker's presence remains in some doubt.
Not keen to take any chances over the fitness of his top scorer, Parkinson says Hanson will only be involved against Barnsley should the striker be deemed completely fit to play.
With Hanson in the team or not though, Parkinson is confident of his side's ability to give their South Yorkshire neighbours a game come Sunday afternoon.
Parkinson said: "There is a question mark over James.
"We left James out of last weekend (vs Crewe Alexandra) thinking he would be a certainty for this Sunday but he has suffered a slight set-back earlier this week.
"As we said before the Crewe game, we will only play James if he is right. If he isn't right, he won't play.
"Even if James is fit, there is no guarantee he will come back into the team. We have proved at Milton Keynes Dons and against Crewe that we can win without him.
"There are other players in the side who are playing well and probably deserve to keep their place.
"If James is fit, will he walk back into the side? That is a decision we will have to make after looking through the week's training, last Saturday's performance and what we've seen on Barnsley. We have to go with how we feel is best to play against them to get the result.
"Either way, we are confident in the ability of our squad to give a good account of ourselves if we get the basics right this Sunday."