With Xabi Alonso out of contract at the end of the season, Los Blancos are reportedly keen to strengthen in midfield, with Gundogan said to be one of their primary transfer targets.
The Germany international has seen his campaign blighted by a persistent back problem but Irfan is confident that talks over a move to the Santiago Bernabeu will begin as soon as Iklay is fully fit.
“Madrid’s interest in my son is considerable and they want to negotiate for him," he told AS.
"But, at the moment, we can’t do anything until Ilkay has completely recovered from his back injury.
"When he is playing regular football we can begin talks.”
Gundogan suffered a recurrence of a back problem on international duty at the start of the season but is hopeful of making his return to action when the Bundesliga resumes in January.