The veteran forward suffered the injury during the Boxing Day win over Chesterfield, and with Daniel McBreen and Ramon Calliste also on the sidelines United have little cover for the first choice strike pairing of Billy Sharp and Andy Keogh.
Adkins hopes to solve the problem by bringing in a player on a temporary basis, but is still unsure how long Torpey - who definately misses the visit of Bournemouth on Saturday - will be ruled out for.
"It's too early to say at the moment how long Torps will be out," he told the Scunthorpe Telegraph.
"We will get all the information we need, but at this moment he is very uncomfortable just to be walking, and the signs are not good.
"With McBreen struggling through injury and Calliste still some way away from full fitness, that does leave us short of cover.
"I would love to bring someone in, and we have identified a number of different targets who we have watched several times