Madrid made major changes to their squad during the summer, bringing in six players, including record signing Yan Diomande, Bernardo Silva and Marc Cucurella.
However, their attempt to sign Rodri failed, leaving Silva as the only major midfield addition following the departures of Luka Modric and Toni Kroos in recent seasons.
Mourinho said he was not looking for any more signings before the transfer window closes.
"For me the squad is closed, but the market is still open," Mourinho told reporters. "You never know if a player will come and say, 'I've been benched twice and I want to leave'.
"In theory no (more deals), but something could always happen. In my head the squad is closed, and I have not asked for anyone. I am very happy with the players I have."
Madrid began their La Liga campaign with a hard-fought 2-1 victory away to Espanyol on Saturday, with Silva and Federico Valverde starting together in midfield.
Mourinho also confirmed that Aurelien Tchouameni would miss Wednesday's match against Real Sociedad because the French midfielder had not fully recovered.
"He's got a problem, the holiday time wasn't enough for him to recover," Mourinho said.
"You can finish a season suffering, the last couple of months, but you can't start in August not at 100%.
"So we decided with him, the staff, the medical department, to get him to return at 100%."
The Real Madrid coach also backed Valverde to play a central role in midfield, despite the Uruguay international having previously been used at right-back and on the wing.
"For me he is a player for the centre of the pitch," Mourinho said.
"Depending on the opponent and our objectives, he might be more set in his position or more mobile."
Mourinho added that modern football had made traditional positional labels less important.
"I don't want to identify Tchouameni as the No. 6, Camavinga No. 6, Fede No. 8, Bernardo No. 10," he said. "Things dilute during games."
Real Madrid host Real Sociedad at the Santiago Bernabeu on Wednesday as Mourinho's side look to make it two wins from two at the start of their La Liga campaign.
Marc Cucurella has officially been unveiled as a Real Madrid player, with the Spain international saying he is excited to experience the Santiago Bernabeu from inside the club rather than as an opponent.
Malaga and Deportivo A Coruna shared the points in a 1-1 draw, while Osasuna and Levante played out a goalless stalemate as the four clubs continued their La Liga campaigns.
Atletico Madrid boss Diego Simeone revealed that he apologized to Nigeria star Ademola Lookman for playing him out of position in the 2-2 draw against Villarreal on Sunday.
Barcelona could be preparing to shift their focus to Nigerian striker Victor Osimhen as their long-running pursuit of Julian Alvarez continues to hit obstacles.
