The London-born 22-year-old came through the Southampton youth academy and has made 29 appearances for the Sky Bet League Two side.
Mansfield confirmed the failed bid and revealed they had rejected an offer from an unnamed English League One team for winger Sam Clucas.
Manager Paul Cox told the club's official website: "Both offers have been turned down flat. I don't want to lose my best players and I'm not in the business of simply giving away players.
"It's a positive in the sense that we've brought through two young players who are being coveted by clubs in higher leagues but we won't roll over and let our players go for what we feel is little compensation."
United, who sold Ryan Gauld to Sporting Lisbon last week for a reported £3million, are looking for defensive reinforcements after losing Gavin Gunning to Birmingham.