Hamburg have told Liverpool and Wigan they can have Elia for £12.5million.
The German outfit want to offload the highly-rated 23-year-old, who is also wanted by Wolfsburg, after the player fell out with manager Armin Veh.
Hamburg, however, are reluctant to allow the player to leave on loan, insisting they will consider permanent offers only having turned down a short-term bid from Wigan.
"We do not loan players out, this is a simple conclusion," said Hamburg sporting director Bastian Reinhardt.
"Also, as the current employer of Elia, we require at least 15 million euros (£12.5m) from potential buyers."