The Manchester United striker's agent, Mino Raiola, offered the Swede to Real at the beginning of the winter market, says El Mundo Deportivo.
It's suggested Perez turned down the prospect, with his prime reason being a reluctance to work with Raiola. Coaching staff also queried whether the Swede would be good for the Real locker room.
The offer was made with Ibrahimovic back on the pitch after recovering from April knee surgery, though is again now sidelined due to complications.
Perez's attitude towards Raiola does put Real's interest in AC Milan goalkeeper Gigio Donnarumma in jeopardy.