The Premier League new-boys returned with a second offer for Jones, 22, after having an initial bid for the Trinidad and Tobago international rejected last week.

Jones hit 16 goals last season to help guide Saints to the Coca-Cola Championship play-offs, where they were beaten by Derby in a dramatic semi-final penalty shoot-out.

Having already lost Gareth Bale and Chris Baird in big-money moves this summer, manager George Burley has no need to sell to balance the books at St Mary's.

A statement on the club's official website, www.saintsfc.co.uk, read: "A further unsolicited and unwelcome approach from Derby County for Kenwyne Jones has been rejected.

"George Burley sees Kenwyne playing a major role in Saints' push for promotion this season.

"Moreover, it is considered that Derby County's latest offer to pay a total of $12million for the player very substantially undervalues his ability and potential as a Premiership-quality striker in the making.

"The club hope the rejection of Derby's latest offer will now bring the matter to a close."

Southampton are reportedly unhappy with the manner of Derby's initial approach for Jones, although the club have yet to comment on whether they are considering taking further action.

Burley reiterated his club's stance, insisting he is only interested in adding to his squad ahead of Saturday's opening game against Crystal Palace.

"I am still looking for a couple more players because we are not quite there yet," said the former Derby boss.