The Yorkshire side turned down an approach from the Shrimpers in the summer, but they have made an inproved offer.
United will be entitled to a percentage of any fee Barnsley receive for Hayes under the deal agreed by the tribunal.
But any hopes of receiving that cash to assist in signing a replacement for Andy Keogh look set to be dashed, with Tykes boss Simon Davey hoping to extend his contract at Oakwell.
"The last thing I'd heard was that Southend had increased their offer for Paul, but it's still no where near our valuation,'' he told PA Sport.
"We paid £150,000 for Paul and their offer is nowhere near that.
"Paul is one whose contract we wanted to extend here. He agreed to extend his contract, but he's a Southend boy and they've put in a bid for him.
"All his family are from Southend and it's unsettled him. He wasn't right to play at Luton so we had to leave him out, but he won't be leaving unless the deal's right for us.''"