Owen has revealed he will leave St James' Park this summer and is searching for a potential club where he can continue his career.
Brown said that although Owen is reluctant to make his way to KC Stadium, the club would do enough to persuade him.
"We will be speaking to Michael's representatives within the week," he told the Hull Daily Mail.
"I would think he would have a number of offers and we'll have to be competitive, but I wouldn't sit down with him if I thought I was wasting my time.
"Anything is possible in football.
"I don't think Michael will go for the best financial offer. I don't think it's about that for him at this stage of his career - he'll want the best offer for his future.
"He needs to spend a high percentage of next season's games at the highest possible level and that's where we can come in."