Joe Daniels was found unresponsive inside his pub the Red Cow, in Foord Road, Folkestone, which is part of the Ei estate, shortly before 11.30am on Wednesday (22 November).
He had suffered an injury consistent with a gunshot wound and was pronounced dead at the scene, police confirmed.
A firearm was recovered from the property.
Senior investigating officer Detective Chief Inspector Richard Vickery, said: "We are continuing to carry out enquiries into the circumstances behind Mr Daniels’ death and cannot yet rule out any third-party involvement.
"I would strongly encourage anyone who saw or heard anything suspicious in the area to call the appeal line urgently."
As of yet, no arrests have been made.
According to Kent Live, bouquets of flowers have been placed in tribute to the 58-year-old outside the pub, with those who drank in the Red Cow describing Daniels as an "absolute legend".
A spokesperson from Ei Publican Partnerships said: “We’re aware of this tragic incident and are assisting police with their enquiry.
"Our thoughts go out to the friends and family of Mr Daniels at this difficult time."
- Anyone with information should call 01843 222289 quoting reference 22-0452, or Kent Crimestoppers anonymously on 0800 555111.