Mourinho, who took over at the Santiago Bernabeu this season, made a beeline for the Bayern Munich midfielder after a tribute match to Germany legend Franz Beckenbauer in Germany on August 13, the daily said.
Shaking the 26-year-old by the hand and looking him in the eye, according to Bild, which didn't cite its sources, Mourinho told him: "I wanted to get you last year, but it didn't happen.
"Next year you belong to me."
Schweinsteiger, a key playmaker in Germany's World Cup -- Joachim Loew's side lit up the championship with demolition jobs of Australia, England and Argentina, finishing third -- could indeed go to Real next year, Bild believes.
His contract at the German giants, who finished runners-up to Mourinho's Inter Milan in last season's Champions League, runs until 2012, and if "Schweini" doesn't extend, 2011 would be Bayern's last chance to cash in, the paper said.
Schweinsteiger, whom Bild believes is worth more than 30 million euros (38.4 million dollars), said previously: "I can't and don't want to say whether I am married to Bayern.
"That wouldn't be fair, including to the fans."
Real paid 18 million euros to get Ozil from Werder Bremem and 14 million for Khedira from Stuttgart.
how many midfielders does Real Madrid honestly.