The Canadian international striker is wanted by both Preston and former club Tranmere Rovers after being put up for sale by manager Mark Robins.
Hume, 26, has struggled to command a regular place at Barnsley since suffering a fractured skull and internal bleeding in a challenge with Sheffield United defender Chris Morgan in November, 2008.
Robins is likely to include Hume, who cost 1.2m from Leicester City two summers ago, on the bench for today's game but a move before Tuesday night's transfer deadline looks inevitable.
"I have had a conversation with Darren Ferguson at Preston and he has expressed an interest in Iain," confirmed Robins. "But we will not do anything until we have the right deal for Iain and ourselves."
Tranmere, the club that launched Hume's career a decade ago, are also understood to be keen but may not have the funds required.
Former Barnsley striker Jon Parkin has been linked with a return to Oakwell from Preston as part of a package deal.
The Tykes are looking to maintain progress after an initially poor start.
Boro, who beat Sheffield United last weekend, raided the transfer market in the summer and are still the bookmakers' favourites to win promotion.
Former Rangers striker Kris Boyd opened his goal account against the Blades and is no stranger to Barnsley defender Jay McEveley because the pair have played together for Scotland.
"Boydy is a natural finisher and his goal-scoring record is a joke," said McEveley, referring to a return of 127 goals in 151 starts for Rangers. "He will probably be the main threat but they have great players all over the pitch."
Boro manager Gordon Strachan is hoping to secure Hamburg's Senegalese midfield international Mickael Tavares on loan. Frenchman Didier Digard has completed a permanent transfer to Nice.