A source close to Perez told the Mirror: "Florentino wants to make Wenger both coach and general manager of Real this summer - and will promise it will happen."
Perez's ambition extends to also signing Gunners skipper Cesc Fabregas and Kaka, from AC Milan.
The Perez contact added: "With Kaka and Fabregas as players and Wenger as coach, Florentino will take Real back to where they should be."
Wenger has twice before stayed loyal to Arsenal and rejected Perez's overtures.
But the dual role - which would mean the departure of sporting director Predrag Mijatovic - would mean far greater control at Real.