The 20-year-old spent the second-half of last season on loan in West Yorkshire where he scored five goals in 21 games in the club's historic Premier League promotion.
The media outlet claim Huddersfield were hoping to take Palmer on loan again, meaning they cannot take another player on-loan from the same side and would therefore have to pay around £8million to land Brown permanently.
However, Southampton are ready to uncomplicate matters by bidding for the England Under-20 star themselves.
Meanwhile, despite landing Jonas Lössl on a season-long loan deal from Mainz on Friday, Town are still in the hunt for a goalkeeper.
And finally, Huddersfield Town are moving closer to sealing a move for Derby County's Tom Ince with BBC Sport suggesting an improved bid has been made for the player.
It is claimed an initial £7m bid was rejected with the club now returning to make an offer closer to Derby's £10m valuation.
However, reports from the Derby Telegraph that a deal could be finalised today for the 25-year-old appear a little pre-mature.