Tim Sherwood insists all of his current squad are playing for their Tottenham careers.
Ralph Krueger has been appointed Southampton chairman just weeks after helping Canada to Olympic ice hockey gold.
The Bundesliga club have been strongly linked with a move for the Croatia international, who joined Everton in January 2012 from Rangers.
Jelavic, who has three years left on his current deal, scored seven times for Everton last season but it is not yet known whether he will be first choice under new Toffees chief Roberto Martinez, who has signed Arouna Kone from his former club Wigan.
Despite an interest in the player, Hamburg insist that a deal is not on the cards.
"It is still a fact we first have to sell a couple of players before we can dig into buying any new," Hamburger general manager Oliver Kreuzer is quoted by Bild.
"And as far as I am concerned we will be unable to finance a deal with Everton FC for him [Jelavic]."