The Tigers travel to Molineux in the Barclays Premier League on Saturday with the transfer window nearing its close and speculation hotting up, particularly following the completion of Joleon Lescott's protracted switch from Everton to Manchester City.
Turner is one of Hull's most prized assets and has been linked with a move away from the KC Stadium for some time after a string of impressive performances since their promotion to the top flight.
Liverpool have enquired about him and Sunderland manager Steve Bruce is the latest to register his interest, but Brown is determined to hang on to his man.
"This centre-half merry-go-round began as soon as Joleon Lescott moved to Manchester City and lo and behold, there are three or four centre-halves that have moved,'' Brown said. "We are trying desperately to hang on to Michael Turner and fingers crossed we can be successful in that area.
"He (Bruce) is not the only one, we've had enquiries from three or four Premier League teams and fortunately we've managed to hang on to him. But the market is so volatile. Twenty-four million pounds for Joleon Lescott just shows you how ridiculous the game has gone.
"People will pay it though, and if they are willing to, there is going to be a cascading effect. Unfortunately we're underneath the big boys and we have to wait for these things to happen.''
After a stuttering start, with defeats against Chelsea and Tottenham, Hull got their league campaign up and running last week with a 1-0 win over Bolton in which Turner's defensive display was instrumental.
Brown said that if the 25-year-old maintained his good form, both he and the club could continue to grow together - but accepted that any big-money offer would have to be considered.
He continued: "Hopefully a win at Wolves will keep Michael Turner at Hull, for a start. But unfortunately all these things take a back seat as soon as double figures in terms of millions are mentioned. Michael was brought to the football club for £350,000 less than three years ago.
"Fortunately for us, we've progressed as a club and he's progressed as a player, but lo and behold, bigger clubs come knocking. It is difficult but it's a fight that we are willing to accept and hopefully we are successful.''
Everton boss David Moyes was highly critical of Lescott's attitude in the build-up to his acrimonious transfer to Eastlands, but Brown has no such concerns about Turner's mentality.
Brown said: "I think he proved that his head is in a good place last Saturday - it was a typical Michael Turner performance in the game against Bolton Wanderers, where you know the ball is going to be in the air and you are going to have to win your aerial challenges against Kevin Davies and Johan Elmander. He did that successfully, we got that clean sheet and it kick-started our season.''
Brown has been looking at several targets himself, and with the signing of Sunderland defender Paul McShane almost secured, he hopes to bolster his forward line before the September 1 deadline.
"We're looking to bring a striker in if we possibly can,'' Brown said. "One or two avenues have been closed to us of late, but one or two more have opened up, so fingers crossed, we will get a striker in before the deadline.''
Before that though lies Saturday's assignment at Molineux, where Brown thinks Mick McCarthy has done well to rebuild his reputation after a dreadful 2005-06 season at Sunderland where they finished bottom of the Premier League with just 15 points garnered all season.
"Mick has done a tremendous job at Wolves, having picked himself up and dusted himself down after the Sunderland affair,'' Brown said.
"He's gone into Molineux and last season was a tremendous year for him. And he's started this year in good form - he's got that first win which is all important away at Wigan, which was no easy feat. We know what we've got to do. I remember going there a couple of years back in the Championship and it's never an easy place to go, and they're on the up.''