The Blues boss has already failed with two bids for the England star, who was cheered by Red Devils fans during a frustrating stalemate despite the ongoing uncertainty surrounding his future.
When asked whether he planned to make a third offer to Rooney, Mourinho said: "We have to speak but this club must be a very special club, because in every club in the world when a player wants to leave, they don't support him. They give him a hard time. But they support him all the way.
"That proves this is a really special club with special fans and I think now he'll decide he wants to stay. If he makes that decision, we will be the first to respect that and say 'it's over.'
"It depends on his reaction, on his feelings. If now, he doesn't want to leave, we are out of the thing. We need to know what is happening."
On the game itself, the Portuguese added: "I think the result is fair. I think nobody did enough to be better than the opponent. I think we controlled the game for most of the time. We did not have real problems.
"Our passing for counter-attack, to go from a defensive situation to an attacking situation, was not the best. We had very creative and fast players in attack but we lost simple passes and made lots of mistake.
"In terms of attack, we didn't give what we could or what we should, but I told the players before the game that we want to win and we would play to win. I think the players understood.
"For me, we didn't create chances because when we recovered the ball we lost so many easy passes. I will watch it on video and find six, seven or eight easy passes to go for counter-attack when the players should and could do more.
"It was a difficult match for them and a difficult match for us. We both wanted to win but we also didn't want to lose. I think it was a really big match but at the end of the day, we have six points from our two matches at home.
"After this difficult start, we are fine. It was also a great experience for our kids - four guys in attack in Edin Hazard, Kevin De Bruyne, Andre Schurrle and Oscar are four babies. To have this experience was very good for them."