The 43-year-old is the heavy favourite to replace under-fire boss Carlo Ancelotti should Real Madrid decide to part ways with the Italian.
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Ancelotti’s side suffered humiliation in the Champions League, losing 5-1 on aggregate to Arsenal, putting his position at the club under increasing scrutiny.
Speaking to the press ahead of Leverkusen’s Bundesliga clash with St Pauli, Alonso insisted he’s not thinking about the future.
He told reporters: “It's not a good time to discuss the future. We're at a very important moment in the season. I don't want to talk about speculation and rumours. (I understand) that this is happening, but what's more important to me is what's happening right now."