In July 2013, he signed for Greuther Fürth, where he spent the 2012–13 season,[4] scoring a goal in 11 competitive matches.[2] He also scored four goals in five matches for the reserve team.[2] Then he joined VfR Aalen for the 2014–15 season.[4] He scored one goal in 26 competitive appearances.[8] In the following season, he scored nine goals in 32 competitive appearances.[9] He then joined Holstein Kiel for the 2016-17 season.[4] During that season, he scored seven goals in 35 appearances.[10] During the 2017–18 season, he scored 14 goals in 34 appearances.[11] This includes two goals in two appearances in the DFB Pokal and an appearance in the Promotion playoff.[11]
Drexler signed with Midtjylland for the 2018–19 season. The transfer fee paid to Holstein Kiel was reported to be €2.5 million.[12] However, during the same summer he was transferred again to 2. Bundesliga side 1. FC Köln for a reported fee of €4.5 million.[13]
On 21 July 2021, he agreed to join Schalke 04, newly relegated from the Bundesliga, signing a two-year contract,[14] which was extended by a further year due to Schalke's promotion in 2022. On 14 November 2023, the contract was extended until 30 June 2025.[15]