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 Bild reported on Tuesday.
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 Löw'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 said is worth more than €30 million ($38.4 million), 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 to get Özil from Werder Bremen and €14 million for Khedira from Stuttgart.