"We made an approach and Lippi turned it down. This is not a stunt. It's genuine," Sullivan told the Birmingham Mail.
"He is available at the moment and we are looking at bringing in a manager of his stature and calibre, if at all possible.
"He was one of the first we went to but unfortunately nothing materialised.
"Of course, you get knock-backs. That's football. But if you do not try you will never know. It was the same with Martin Jol. It made sense for us to approach him.
"We are juggling other balls in the air at the moment and we will see which ones land. I want to stress to our supporters that we are working very, very hard to bring in the right man.
"Until you get to meet them and speak to them, you can never be quite sure. But it won't be for a lack of trying, believe me.
"We are determined to find a manager who would create a bit of a stir and excite people."