The pictures show him wearing an orange jacket with the hood up. He was also wearing black bottoms and white footwear.
Police said that anyone who knows the man or who has information that could help should get in touch with them.
Mr McMurchie, a Dundee United fan, spent Saturday evening in city pubs including the Dolphin Bar, the Balmore Bar and the Albert Bar and then went to an address in Murrayfield Gardens. He left the house between 3.30am and 4am.
Police have previously urged any pub-goers who saw him during the night to get in touch. Last month they also appealed to football fans for information during a match between Dundee United and Dundee at Tannadice Stadium.
Tayside Police can be contacted on 0300 111 2222 or information can be passed to Crimestoppers anonymously on 0800 555 111.