The silky playmaker was a late addition to his nation’s World Cup squad after injury struck Croatia, and has long been hailed as a top talent.
Despite Hamburg’s domestic woes last term Badelj’s stock has remained high, which has attracted Chelsea and Spurs.
HSV would ideally like to keep the classy passer, but they are aware that interest from big sides will bring a large fee.
The Blues have already bolstered their midfield by adding Cesc Fabregas, but Jose Mourinho is understood to be targeting further signings as he sets about securing domestic and European honours.
Tottenham are also in the battle with Mauricio Pochettino still looking for his first addition since swapping Southampton for north London.
Badelj won four league titles in his homeland before joining Hamburg and netted once in 29 showings last season.