Koke, who was speaking at a LaLiga end-of-season event, said he had deliberately switched off from football news during a break in Menorca.
"I've been there with my phone off, with my wife, after a very intense year with many matches and many stories," he said. "I don't know about any meeting. The only thing I know is that Julián is an Atletico Madrid player. He has a contract until 2030 and a release clause worth many millions. That is all I can tell you."
He was asked whether an Álvarez move to Barcelona would disappoint him personally.
"Julián, as I've told you — he's an Atletico Madrid player. He's a lad who is giving everything. He's been at the club two years. Everyone, since he arrived, has been selling him to Barcelona, to here, to there. Right now he is an Atletico player — unless he comes out and says otherwise himself."
Barcelona submitted what is understood to be an opening offer of around €100 million, which Atletico dismissed immediately. The Catalan club are reportedly willing to increase the bid to €135 million with variables, but Atletico have consistently maintained that the striker is not for sale. His release clause stands at €500 million and the club's stated valuation is well above €200 million.
Álvarez missed the final four matches of the season with an ankle injury sustained during the Champions League semi-final defeat to Arsenal on May 5.
On his own future, Koke — who is 34 and whose current deal covers next season — gave little away but suggested an announcement was imminent.
"Why only one more year? We are working on it. Soon we will say something. I'm not going to tell you here — if there is something to do, it will be done properly, and we will say something soon."