Hamburg endured a poor season last campaign and only just survived relegation, there are bound to be changes made in the side and although Badelj is an important part of the team, the club could be forced to cash in to rebuild.
Chelsea have already strengthened ahead of the new season with the arrivals of Cesc Fabregas and Diego Costa, with Fabregas brought in to improve The Blues midfielder following Frank Lampard's exit.
However, David Luiz has also left the club and played in the defensive midfield role that Badelj plays too, so a move for the Croatian would make sense as Jose Mourinho looks to build a side capable of winning the Premier League title this season.
Spurs have an abundance of talent in the middle of the park, but with Sandro's future far from clear Mauricio Pochettino could move for Hamburg's enforcer.
The Lilywhites have seen many Croatians at White Hart Lane over recent years with Niko Kranjcar, Vedran Corluka, Stipe Pletikosa and Luka Modric all playing for the club and Badelj could be the next name to add to that list.
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Badelj was a part of the Croatian World Cup squad in Brazil this summer, after some solid performances last season saw him make the final 23-man squad.
The midfielder score one goal in 29 appearances last season, but won almost three tackles per game with an average pass completiton rate of 81%.
He would certainly give Spurs or Chelsea more options with a switch to the Premier League but Hamburg are likely to hold out for a top end valuation on their man.