The Belgium goalkeeper was forced off during Belgium's World Cup quarter-final defeat to Spain this summer, and has spent the following weeks working to ensure his fitness before rejoining full training. He trained alone at Real Madrid's Valdebebas complex on Sunday, with the rest of the first-team squad given the day off following the club's pre-season friendly win over Ferencvaros.
"In the end I came back a bit early because with the injury I wanted to make sure everything was okay and train individually for a few days before starting with the team," Courtois said.
The 34-year-old, who worked under Mourinho during a Premier League-winning spell together at Chelsea, said he was looking forward to being coached by the Portuguese again at Real Madrid.
"He's a coach who demands a lot. Discipline, the group before the individual, these are important things for winning.
"He's a great coach. As a person he's very approachable, he says things as they are and I like that honesty, it's the direction we have to take," Courtois said. "We coincided at Chelsea, we won the Premier League, I have good memories of him and I'm happy to be under his orders again."
Looking ahead to the new campaign, Courtois said he was eager to return to winning ways after a difficult recent period, with Real Madrid having missed out on major honours last season.
"With a lot of enthusiasm, I want to win titles again, it's important for the team, for the fans and for the club," he said. "There are quite a few new players, some we know from having played against them. We're keen to be all together again after the World Cup and fight for a new season."
Courtois is one of several Real Madrid internationals still working their way back into full training following an extended summer, with the club's pre-season schedule continuing ahead of the new La Liga campaign.