The Spaniard has a contract with Leverkusen until 2026, and his team are currently top of the Bundesliga, eight points clear of champions Bayern, who on Wednesday said they would part ways with coach Thomas Tuchel at the end of the season.
Leverkusen are unbeaten across all competitions this season as they eye their first-ever Bundesliga title that would end 11 years of uninterrupted Bayern dominance in the league.
Tuchel's end-of-the-season departure from Bayern has fanned speculation regarding Alonso possibly succeeding him with the Leverkusen coach having played for Bayern from 2014-17.
"Maybe you have questions about my future but I have nothing new to say about that. I wanted to say that in advance," Alonso told a press conference.
He has also been linked with a possible move to Liverpool with current coach Jurgen Klopp stepping down at the end of the season. Alonso also had a successful spell at Liverpool from 2004-2009.
"For me, this (speculation) is not a problem," he said. "I know that my goal is to be successful with my team.
"That is my job. We are currently in a good position and we want to keep at it."
"It is normal to have questions but it is not an issue for me."
Asked whether he would be coach of Leverkusen next season as well, Alonso said: "That is what I assume."
Leverkusen host Mainz 05 on Friday.
