Steven Caulker left Dundee United last week and Celtic should look to sign him on a free transfer.
The 26-year-old defender activated a clause on Friday that allows him to leave the club as a free agent.
Celtic could do with some defensive depth and Caulker would be a useful option. The former England international has plenty of experience at the top level.
Apart from his defensive ability, Caulker would provide Rodgers with more options. His arrival would allow Celtic to rotate at the back.
Furthermore, he has worked with Rodgers before at Swansea City.