As exclusively revealed in The Star this week, the Reds tabled an initial offer for 23-year-old Nelson who has been offered a new contract to stay at Home Park.
But the Pilgrims labelled the bid “derisory” in an official statement released on their official website.
The statement read: "Following newspaper reports linking Barnsley with our captain, Curtis Nelson, we can confirm that we have rejected a derisory offer from them for the player.
“Curtis remains under contract to us and any approach to him without our approval would be in contravention of EFL rules.”
Providing Nelson wants to leave and, if the two clubs still cannot agree on a fee, any proposed move would be handled by a tribunal.
Meanwhile, long-serving Academy Manager Ronnie Branson has left Oakwell to “pursue other footballing opportunities” a brief statement on the official Barnsley FC website read.
Branson has been the club’s Academy Manager since 2006 and played a key role in developing some of the club’s best young talent, including John Stones, Mason Holgate and James Bree.