The deal is said to be worth potentially upto £150,000 on appearances and if he becomes an international.
Lennie has admitted his interest and confirmed he will be watching 22 year old Bullock in action for York City next Sunday when they entertain Huddersfield.
"We are still interested in Lee Bullock and I will be going up to watch him play for York."
Bullock is a highly rated attacking midfielder and has been linked to City before.
Lennie has still not ruled a possible move for Andy Monkhouse and despite denials from Cambridge Utd yesterday Lennie has said he is keeping an eye on Luke Guttridge and will be tracking him for the rest of the season.