Klopp made the surprise announcement on Friday he would leave the club he joined in 2015, saying he was "running out of energy."
Alonso, a former Liverpool player whose unbeaten Leverkusen side sit four points clear of Bayern Munich at the top of the Bundesliga table, has been linked to a return to the club where he won the 2005 Champions League as a player.
Saying the "speculation is normal", Alonso told reporters: "At the moment I am really happy here... I'm not thinking about May, I'm thinking about tomorrow's game.
"Each day is a challenge, each game is a challenge and were are on an intense and beautiful journey here in Leverkusen."
German media has reported 42-year-old Alonso has a clause in his contract that allows him to leave for one of his former clubs - Liverpool, Real Madrid and Bayern Munich - should an opportunity arise.
"I am not thinking about the next step," he said.
"I am thinking about where I am right now – I am in a great place and I am enjoying myself. And I think it's the right place, so that's all I can say.
"What's going to happen in the future? I don't know and I don't really care at the moment."
Alonso praised Klopp, saying he has "huge respect and great admiration for what Jurgen did for the last nine years in Liverpool - and how he did it."
Leverkusen have dropped just six of a possible 54 points this season and have won every one of their Europa League and German Cup fixtures. They face Borussia Moenchengladbach at home on Saturday.