West Midlands Police say the 51-year-old was released after the person who placed the Wolves top chose not to make a formal complaint.
Tributes including flowers and Wolves clothing have been placed outside The Clifton pub, on Bull Ring, near to where Mr Cox died following a violent street attack this month.
Six men have been charged with the murder of Mr Cox - a Wolves fan and young father - while another man has been charged with violent disorder and actual bodily harm.
A spokesman for West Midlands Police said: "A 51-year-old man arrested on suspicion of theft has been released with no further action.
"We’ve since spoken to the person who placed the tribute and they don’t want to make a formal complaint. Taking this into account there is no longer an active investigation.
"Our thoughts remain with the family and friends of Reece who’ve suffered the loss of a loved one so young."