Alarcon insists they're happy to continue with the Chilean, now 72.
He said on Cadena SER: "The coach's contract was renewed, we set the timeline, and since then, that issue hasn't been up for discussion.
"It doesn't concern me or occupy my time. In all the scenarios and financial plans we're considering for next season, Mr. Manuel Pellegrini is the first name that comes up.
"I understand the public debate, but it's not a discussion taking place within the sporting committee."
On the prospect of qualifying for the Champions League, Alarcon added: "Our base budget is Europe. If we qualify for the Champions League, we wouldn't do anything crazy because you can't spend on a squad that you can't maintain if you don't repeat the feat.
"Missing out on Europe would definitely damage our planning and force us to reduce the cost of the squad."