The 24-year-old joined the League One side on an emergency loan deal in September.
"We are down the line in terms of reaching an agreement for January," Jackett told Wolves' official website.
"James likes the club, he is happy here and wants to come. He has done well and we've missed him over the last couple of weeks with his injury. He gave us a burst of energy and has got a few goals as well."
Henry has scored three goals in nine appearances for the Molineux club.