Darren Smith, 51, was last seen in the Warren Place area of the city at around 3.30pm on Wednesday, May 28.
Police believe Darren may have been travelling to Milton Keynes.
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Officers have been carrying out extensive enquiries to try to locate Darren, but are extremely concerned for his welfare, and are now turning to the public for assistance.
Darren is described as white, approximately 5ft 9 inches tall, medium build with grey hair and a beard.
In a statement, a spokesperson for Hampshire Constabulary said: “If you think you’ve seen Darren since he went missing or think you might know where he is now, please call us immediately on 999 quoting 44250237348.”
