Brown has been in discussions with the 34-year-old, who is said to be considering offers in England and abroad after falling out of contract at Portsmouth.
The former England international would be an ideal replacement for Turner, who has been earmarked for a switch to Anfield.
However, with the Merseyside outfit having not yet lured the Tigers' star defender away from the club, a move for Campbell may not be necessary.
Brown admits he has held talks with the experienced defender but insists no deal has been done.
Conversation"I've had a good conversation with Sol Campbell," Brown told the Hull Daily Mail. "It was obviously in protection if I lost Michael Turner.
"We might have priced Michael or ourselves out of the market with regards to his valuation but if that's the case, then I'll be delighted.
"If it's not the case and someone is willing to meet our valuation, I'll need a centre-half.
"I spoke with Sol because I was allowed to speak with him, he's not contracted to another club, but that doesn't mean to say it would come cheap.
"He's certainly of interest to me if I was to lose a centre-half, but at this stage there's nothing new to say on Michael."