"I don't know if anyone knows how things ended [between us]," Rooney told national newspapers.
"We had differences [of opinion]. That's normal. Ask Roy [Hodgson, the England manager] -- he's had differences with other players. That's part of football. I'm not the only person who had differences with Sir Alex Ferguson, but I can still sit here and say he was the greatest manager of all time.
"I still see Sir Alex quite a bit at games and he travels away to European games with us. It's not that we don't like each other. We just had differences. That's normal."
The Argentina international, who was criticised for his display in United's 2-1 loss at Swansea, told La Nacion in quotes reported by The Sun: "Playing for United is a dream and if God helps me this dream will never end.
"As I have been saying: I have to thank Van Gaal for trusting me. But let me tell you, I don't think that the goalkeeper spot in United is already mine. I do know that I have a huge support from Van Gaal and his staff."
Reflecting on his move to Old Trafford, which came after his contract expired at Sampdoria, Romero added: "Although I had not done a preseason, I started playing for the biggest club in the world.
"It's important for a goalkeeper to have this support. That is because there is no rotation between goalkeepers -- a goalkeeper starts or he is benched.
"They are the only two choices -- there is not a third one. And Van Gaal has given me his trust."
"My relationship with him is normal, just like all the players. I don't think he had this business with Brazilians, no," the 2015 Under-20 World Cup runner-up said on Monday.
"Everyone says that he sends Brazilians away, it's not so. He treats me normal and equal to everyone. I don't think he has anything against Brazilians.
"Everyone can say what they want, but with me it's going good."