Teamtalk are reporting that Lee, 30, is close to sealing a move to Bradford, after being released by Doncaster this summer.
The article suggests that Stuart McCall has beaten off stiff competition from Scunthorpe and League Two rivals Shrewsbury- where he spent a period on loan last season.
Adkins is keep to strengthen his backline after losing Andy Butler on Friday, and the latest developments seem as though he has faced another setback in strengthening his squad.