So far Liverpool have failed to improve on their initial offer - though to be around half of Hull's £12m valuation - but Brown has acknowledged the fact that he will struggle to hold on to the 25-year-old.
Having struggled to complete a number of signings this summer, Brown will no doubt want to ensure he has a solid back line to ensure the club's Premier League survival which has resulted in him approaching Campbell.
The 34-year-old, who is a free agent after his contract with Portsmouth expired at the start of the summer, is understood to be considering offers in England and overseas, but Brown considers him the ideal replacement for Turner.
"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."
With the close of the transfer window rapidly approaching, Hull have also been linked with making a move for Celtic full-back Andreas Hinkel.
Brown is said to have watched the German play in Celtic's pre-season friendly against Cardiff, but denied he was only there to monitor Hinkel.
"We've had a look at him," he said after the match. "We've watched Celtic and it wasn't to go see Hinkel. Whenever you go see a game of football, you're always looking at every position and he did well.
"People know we're in the market for a right-back."