His incredible pace made him one of the most dangerous attackers in the Third Division, but he failed to keep in form for the full season. He made 47 appearances for City in all competitions.
With Jan Molby looking to play a 4-3-3 formation the speedy winger would find it hard to fit into the new system. Another factor could also be that he is based in Lancashire, and Molby said that the suggestion of him staying in Hull during the week was "not ideal".
Beresford joins Nicky Mohan, Rob Matthews, Mike Price and Lee Philpott on the transfer list. The club are not seeking a fee for any of them.
Plymouth are reported to be interested in Beresford after hearing today's news, but there is no official word from Home Park.
Meanwhile Scarborough are rumoured to be still interested in signing Neil Mann. They twice took him on loan last season but he made limited appearances due to injury.