BBC Sport has reported that young Lincoln City defender Kern Miller is training with the Reds with a view to a move next month.
The 19-year-old's contract with Lincoln runs out this month but wouldn't be able to play for the Reds until the New Year if he signs.
Imps boss Steve Tilson told BBC Radio Lincolnshire:
"We're in the process of offering him a two-and-a-half year deal but he's been training for a couple of days at Barnsley.
"He's out of contract in December which isn't fantastic for us. At the moment he's keeping his options open but he could well go to Barnsley."
Tilson added: "Since I've come in he's done well which is why I've offered him a new contract but we'll have to see.
"If Barnsley do take him we could get compensation and a sell-on clause [in the deal] but that's more out of courtesy because they don't need to give us anything."
Miller has only made one first team appearance for Lincoln and was involved in an incident on a night out in Blackpool which saw him end up with a broken jaw.