However, he has chosen to stay to the club that gave him a chance as a young 42-year-old coach.
"It's been a season we have had a lot of speculation regarding my future," said Alonso to reporters.
"Until now we have had so many games, been pretty busy and focused, and I wanted to reflect during the international break and take a decision.
"And last week, I had a very good meeting with Simon (Rolfes) and Fernando (Carro) when I informed them of my decision to continue being coach of Bayer Leverkusen.
"For sure, all of the decisions you need to analyze well. I try to take the right ones, I try to take them in a natural way and at this moment I felt that this is the best place for me to be, for me to develop as a coach.
"I am a young coach but I have to feel it, right now I feel this is the right place. I have to thank the management, the club has been really, really supportive and I feel really respected by all of the departments.
"The fans showed great support during last year in difficult moments, I felt that, and they have all the reasons to believe and to dream that we can have a great season, and we are really pushing for that.
"Great staff help me day by day to work better and improve and to prepare the team. And, for sure, the players. They gave me so many reasons to keep believing in the team; their commitment, their desire, their hunger to have a great season.
"I feel my job is not over here and I want to help them, I want to help the team, I want to help the young players develop. And if I am part of the process, I am happy with that."