The 25 year-old has featured for his country at the World Cup in Brazil and sources close to the Bundesliga man claim he is looking to move to an English club.
Although Hamburg see him as a valuable player who they will not want to lose, the German side could be tempted into cashing in for the midfielder if a large sum of money is put forward.
Chelsea boss Jose Mourinho has already shown he is keen to bolster his midfield with the signing of Cesc Fabregas and definitely needs to re-strengthen his defensive midfield following the departure of Frank Lampard and David Luiz.
Meanwhile, new Spurs boss Mauricio Pochettino is looking to bring in new signings to revitalise the team which only managed a 6th place finish last campaign.
Badelj has won four league titles with his previous club Dinamo Zagreb and scored one goal in 29 appearances for Hamburg last season.
By Phil Wellbrook