The Oakwell outfit are keen on adding the former Leeds United player to their squad, but their advances have been spurned by the Spireites, who are understood to have snubbed a third offer.
Spireites boss Wilson said: “We received an offer from Barnsley for Gboly, which can only be described as derisory for a player of his ability and potential. The offer was rejected out of hand.
“I am keen to keep Gboly as he is very much part of my plans and I know that the board share the same view.”
USA-born Ariyibi, 21, is in the last year of his contract at the Proact Stadium and is unwilling to consider a longer-term deal, as it stands.