We never know the exact reason why Leverkusen recruited Ten Hag after Xabi Alonso decided to join Real Madrid but some speculation emerged and Leverkusen himself chose Ten Hag for its success in winning three league titles and two domestic trophies with Ajax. This reason did not strengthen because after becoming Manchester United coach he actually failed even though his first season went much better at Manchester United. Jose Mourinho is also not an old ideal choice in my opinion because his abilities are no longer the same as the previous seasons, and I agree more if Leverkusen tried to recruit former Dortmund coach because he better understood the characteristics of the Bundesliga.
Leverkusen should consider a coach with Bundesliga experience over one with experience from other leagues. Leverkusen desperately needs a tactical approach to improve their players overall, as the current players aren't as promising or star-studded as those at other teams. Therefore, Leverkusen can't afford to make another mistake in choosing a manager so they can develop slowly without having to repeatedly fire managers. And if you mean Edin Terzic, I think he is also a very good option for Leverkusen this season.