The Sun says Perez and his director general Jorge Valdano have held summit talks over a £43million summer bid for the midfield ace - and how they can knock deadly rivals Barcelona out of the running.
Against that, Barca hope to weigh in with a straight £40m bid.
If that fails, an alternative is to offer unsettled Ivory Coast midfielder Yaya Toure, brother of former Gunners defender Kolo, plus £30m.
Barca president Joan Laporta has already promised "to fight for the kid" who played for the club as a teenager.
A Real insider revealed: "The price demanded is £43m and that is what we are basing our calculations on.
"This is 'Operation Cesc', which we hope will prove a blow to Barcelona."