The 28-year-old cost Arsene Wenger in the region of £12million when he moved from Malaga last summer, with the player going on to score 12 goals in his debut season at the Emirates.
Reports on Wednesday claimed Atletico chief executive Miguel Angel Gil Marin had opened discussions with the Gunners over a possible £17.5million deal to take Cazorla back to Spain.
However, when quizzed about a possible deal for the former Villarreal star, Cerezo denied Atletico had made a bid.
"We have no news of Cazorla," he said. "These are invented stories that are made up every day."
Atletico signed Cazorla's former Malaga team-mate Martin Demichelis earlier this month, with the Argentine agreeing a one-year deal.
Los Rojiblancos, who finished third in the Primera Division last season and won the Copa del Rey, have also signed forwards David Villa and Leo Baptistao already this summer and brought back goalkeeper Thibaut Courtois for a third year on loan from Chelsea.