Boro manager Neil Warnock worked with Brown in his time as Cardiff manager, and has admitted he would like to take him to the Riverside, where the Championship side are light on the left-hand side of defence.
A bid has been lodged, but McCarthy says it falls well short of the Bluebirds' valuation of the 23-year-old, who is in the fnal year of his contract.
"I don't want to sell Browny, I've offered him a new contract and I'd like him to stay," revealed the former Barnsley centre-back.
"I've spoken to Neil, he's made an offer. Nowhere near enough.
"Browny is in his last year (of his contract). So if Neil wants to offer something that's anywhere near our valuation, even though the player has only got 12 months to run, then we may have to sell him. We don't want him to go on a free transfer.
"If not, he'll stay here on the contract he's on until the end of the season.
"I expect he will play and continue to play and compete just like he always would."
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