As Klein holds a German passport, he is not considered an overseas player in English domestic cricket.
[2] In February 2019, Klein attended a training camp with the German national cricket team, with a view to help Germany qualify via the Regional Finals of the 2018–19 ICC World Twenty20 Europe Qualifier group for the 2020 ICC T20 World Cup.
[3] In May 2019, he was named in Germany's squad for the Regional Finals of the 2018–19 ICC T20 World Cup Europe Qualifier tournament in Guernsey.
[6] In September 2021, he was named in Germany's T20I squad for the Regional Final of the 2021 ICC Men's T20 World Cup Europe Qualifier tournament.
[7] In January 2022, he was named in Germany's team for the 2022 ICC Men's T20 World Cup Global Qualifier A tournament in Oman.