Vuskovic, 18, joined Tottenham two years ago after the club agreed to sign him. He has been an unused substitute in all three of Tottenham's games this season, but showed promise in a pre-season win against Reading, scoring a goal and providing an assist.
It's likely that Vuskovic will join Hamburg on loan, which will give him regular playing time and a chance to prove himself to manager Thomas Frank.
Meanwhile, Galatasaray is in talks with Tottenham over a loan deal for midfielder Yves Bissouma. Bissouma, 28, was signed from Brighton for £25M in 2022, but has not been in Tottenham's squad for their two Premier League matches due to an injury.
Bissouma is out of contract with Tottenham next summer and is not in Frank's plans, despite making 100 appearances for the club, including starting in the Europa League final win over Manchester United in May.