The Wales international has been linked with a move to United amid talk of Madrid's pursuit of Monaco star Kylian Mbappe.
Mourinho said he would consider Bale to be available if he were left on the bench for the UEFA Super Cup against United on Tuesday, but the 28-year-old started alongside Karim Benzema and set up Isco to score his side's second in their 2-1 victory.
And the United manager accepts that any chance of bringing the former Tottenham man back to the Premier League appear to be over.
"I think so, I think clearly the club wants him, the manager wants him, the player wants it," he said. "I think game over. Because I think now he's going to stay."
Bale himself stressed that his focus is on playing for the European champions and made it clear that he has not spoken with the club about the prospect of a move away.
"I'm just concentrating on my football," he told BT Sport. "I'm not listening to anything. I don't read anything.
"Obviously I get told bits and bobs but I'm just enjoying being here, playing as much as I can and winning trophies.
"I haven't had any of those conversations [with Real Madrid]. I'm trying to get my fitness up pretty much after not playing fully for eight or nine months."
Casemiro and Isco's goals secured the win for Madrid in Skopje, despite Romelu Lukaku scoring on his competitive United debut.
Zinedine Zidane's side have won the trophy three times since 2014 and claimed six major titles since the Frenchman took charge in January 2016.