Turner has been linked with Liverpool and Tottenham Hotspur over the summer after impressing for the Tigers during his debut season in the Premier League.
Brown has said that it would take a 'ridiculous' offer to convince him to sell the 25-year-old, with reports claiming Hull would demand £12million for the centre-half.
Speculation continues to surround Turner's future at the KC Stadium and Brown acknowledged there has been further interest while the club have been competing in the Asia Trophy in China.
"That's certainly not the case," Brown told the Hull Daily Mail when asked if Liverpool had made a bid.
"We've been here for six days and speculation is rife back at home.
"There has been interest for Michael Turner while we've been away, but still no firm bids.
"It's one of the clubs that previously showed an interest, but it's well documented that a number of big clubs have got problems with centre-halves."