The Scunthorpe Telegraph reports that Hayes was on the verge of joining the Oakwell outfit last weekend, only for another club to enter the frame for his signature.
The contract saga has dragged on since the turn of the year, when the Iron made their first offer.
But Hayes could now be set to join Andy Ritchie's side by the end of the week, ending his two-and-a-half year spell at Glanford Park.
Iron boss Brian Laws has given the striker a deadline of this weekend to decide whether he is staying in North Lincolnshire or not.
Due to Hayes' age the Iron will receive compensation, likely to be set by a Football League tribunal, and Laws will now be looking to act quickly to sign a replacement.
Last week he held talks with two strikers with a view to replacing the 20-goal frontman.