Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
Wolfsburg director of sport Klaus Allofs says the club are keen to hold on to both Bas Dost and Nicklas Bendtner.
The 23-year-old Hungarian joined the Hammers in February 2009, initially on loan, from Ujpest FC.
He made his only first-team appearance as a substitute in a 4-0 Premier League defeat against Manchester United the following December.
A knee injury ruled Kurucz out of the entire 2010/11 season but he returned to action this term and made 11 appearances on loan at League One Rochdale.