The design, which shows a policeman with a ghetto blaster below the slogan ‘HMP HOP’, has been spotted in Waterloo Road, signed by graffiti artist, Skore.
Councillor Paul Birch, who first noticed the graffiti, said he was unaware of it having been there previously.
He said: "This has all the characteristics of a Banksy, with the police character and the black and white with a splash of colour.
"But realistically, the chances are it’s by a graffiti artist named ‘Skore’ who is a local artist working in the same school and tradition as Banksy.
"But whoever the artist is, I hope this excellent street art isn’t interfered with.
"It has been done very discreetly in a location that is not central and also, unlike unsightly tagging, it actually adds to local culture rather than taking anything away."
Banksy, whose identity remains unknown, has been prolific since the early 1990s for satirical street art combining dark humour and graffiti executed in a very distinct stencilling technique.
His works, which often involve political and social commentary, have appeared – often overnight without warning – on streets, walls and bridges throughout the world.
Councillor John Reynolds, speaking personally as a longstanding member of the Arts Council UK, said: "I very much hope it is a Banksy, and it would be great if he has visited the city.
"I appreciate it may not be to everyone’s taste.
"However, in the meantime we must ensure we preserve the artwork whilst checks are carried out, make sure it is not removed and perhaps in the long term ensure its preservation."
According to a report in the Mail on Sunday in 2008, Banksy is commonly believed to be artist Robin Gunningham from Bristol, although speculation still surrounds the artist’s true identity.