Real Madrid made an enquiry for the former Atletico Madrid forward in the summer, but were told he would not be sold.
The Observer reports that the 25-year-old is now on top of Real Madrid's shopping list for the January transfer window.
Real Madrid are expected to make a bid of more than the £38million City paid when he joined the club from Atletico Madrid two years ago.
Aguero has insisted that he is happy at City.
"I'm very happy at City, very happy since the day I came," he said. "I knew that the project was good and in my head there is nothing else but Manchester City, so how long I'm going to be at City is just never a question.
"I'm happy here, my family's here when they come to England, all I can do is give everything I have for the club and concentrate on achieving for the club.
"We are improving every year the team, the club, the club is growing, we are working in the same direction to get the club as high as possible. Some years are better than others, but it's a much better club, a much better team than it was four or five years ago, so we just have to go [continue] in the same way."