Even if we consider Liverpool as a rich team but they are not going to have Xabi Alonso easily. In fact, Xabi Alonso is not a cheap option for any team and even if we consider Real Madrid as a team that wants to hire Xabi Alonso we can understand that are some teams like Liverpool and Real Madrid, and even Bayern Munich they are all linked to thing Spanis coach which can make the transfer much harder because regardless of dealing with Leverkusen to make them accept this deal, they have to race with beasts like Real Madrid for Xabi Alonso.
However, can't be sure if Xabi Alonso can still have a good performance in Liverpool or not if he leaves Leverkusen.
I don't how much to spend money for signing Xabi Alonso. But it is about the competitors that have the same hope for signing Xabi Alonso. Sure, Xabi Alonso is linked with Liverpool, Bayern Munich, and Real Madrid. These are 3 big teams, there must be a tight competition for signing him. Moreover, Bayern Munich is in urgent to have a new coach. So, they will try all out to sign Xabi Alonso.
I think a manager like him will give his best in any team. If he becomes the manager of Liverpool, I'm sure Liverpool will play better.