Punto Pelota reports that Perez is willing to consider offers from Premier League clubs if Casillas makes it clear he wants to leave. Arsenal and Manchester City have both been strongly linked with the Spain international within the last month.
Casillas has been replaced by Diego Lopez as Madrid's starting keeper for La Liga matches, and while he remains first-choice in the Champions League, the World Cup-winning captain wants his place back in the league starting eleven.
And Perez is willing, in recognition of the 31-year-old's loyal service to the club, to facilitate a deal providing Casillas moves to a Premier League club.
The report states Perez will first of all attempt Casillas to stay, but the two have an agreement whereby Casillas would be able to leave if he fails to regain his starting spot by the end of the season.
His favourite destination is thought to be the English top flight, with Arsenal and City believed to be the front runners.
Joe Hart has come under considerable scrutiny in recent weeks following a series of high profile mistakes, most notably in City's recent 3-1 Champions League defeat at home to Bayern Munich.
But Arsenal similarly have a question mark hanging over their goalkeeping situation, with current first-choice Wojciech Szczesny not entirely comfortable as undisputed number one.
He was dropped for a short period last season - Wenger revealed concerns over his 'mental state' - and the Poland international is prone to errors.
The report makes it clear Casillas is extremely unlikely to leave in the January transfer window, but the likes of Arsenal and Manchester City could be willing to wait until summer for a player of Casillas's calibre and experience.