If this was any other coach, I think they were going to choose the money. I actually like that he has not done that and I also think he is trying to "sharpen the axe" so to say.
You're right. It is quite surprising Xabi Alonso doesn't want to take the chance to be a manager in a better team. He must get higher salary and bigger chance to win prestigious trophies if we moves to Bayern Munich or Liverpool because they have better squad and great club management. However, Xabi Alonso prefers to stay with Bayer Leverkusen and he risks his career there. His loyalty with Bayer Leverkusen may lead him to fail in managing Bayer Leverkusen for the next season. The top teams may be no longer interested in him if Bayer Leverkusen performs badly in the next season. So, it is very brave that Xabi Alonso decided to stay.
Maybe by giving Leverkusen one more year, he will be able to gain more experience before going to a big club, which is actually needed in my opinion. As a coach who is pretty new to the scene, he should think about what will be best for him in the long run.
He probably wants to prove that he really has a great ability as a football manager. He will show people who doubt him that the great performance of Bayer Leverkusen this season isn't just a coincidence. And Xabi Alonso expects that he can make a history in UCL with Bayer Leverkusen. He should have a big dream with Bayer Leverkusen for the next season.
You know, if he right now goes to an English Premier League club and performs badly, it is pretty certainly going to be the end of his glory days.
It is not a must to move to EPL. Not only Liverpool which is very serious to hire Xabi Alonso, but Bayern Munich is also serious to hire him. Xabi Alonso can choose Bayern Munich if he wants to leave Bayern Leverkusen. But Xabi Alonso prefers to stay, he doesn't want to disappoint fans and club management.