Cerezo made the comments at the opening of the Sports Summit Madrid, repeatedly referring to the forward as Julian Lopez throughout his remarks to the assembled press.
The Atletico Madrid president pointed any interested clubs towards Alvarez's contract, which contains a release clause of €500m.
Cerezo also confirmed that an offer had arrived from Real Madrid president Florentino Perez, though he declined to dwell on the details of Atletico's response.
"Yes, the offer from Real Madrid's Florentino arrived, and you already know what was said to Real Madrid. You keep wanting to repeat this constantly and one gets tired of it."
The Atletico president made clear that any club hoping to sign Alvarez would need to meet the terms of his contract in full.
"Julian Lopez is a player of Atletico, and whoever wants Julian Lopez should come, look at the contract, and if it interests them they will take him; and if it doesn't interest them, they won't."
Cerezo went on to dismiss the speculation surrounding the player as a recurring summer story that has become tiresome for the club.
"It seems to be the story of the summer. You all know exactly how the situation stands. He is a player of Atletico Madrid and I believe he will continue to be a player of Atletico Madrid."
He reiterated that the club had received no indication from the player himself that he wished to leave.
"And if not, whoever wants to come and look at the contract. We have no knowledge of that, I repeat it again. We have no knowledge of anything, we have a contract with the player and if someone wants him, let them come, let them talk and we will show them the contract."
Cerezo added that he considered the matter closed for now, regardless of continued reports linking the forward elsewhere.
"And if it interests them, he will leave. Let's be done with this Julian Lopez story. Julian Lopez is a player of Atletico Madrid. Is that clear? Well, that's it. The day he isn't, you will know."
Real Madrid's reported offer of €150m was rejected by Atletico, who have also turned down previous interest from Barcelona over the past month.
Alvarez, who joined Atletico from Manchester City in 2024, is currently away with Argentina at the World Cup and has yet to comment publicly on his own future.