Officers want to speak to the man, pictured, after purses and bank cards were stolen from unattended bags in Chichester city centre around lunchtime on Saturday, March 2 and Saturday, April 13.
Sussex Police said the items were used in nearby shops and pubs, before being used to buy a single rail ticket to Havant on both occasions.
It is believed the man could live in the Havant area.
PC Darren Hughes said: ‘If you think you known this man, please get in touch with us, either online or by calling 101, quoting Sussex serial 0297 of 03/03.
‘You can also contact the independent charity Crimestoppers anonymously on 0800 555 111.’