Laporte is prepared to leave City after the Euros and has been linked with Barca.
But El Confidencial via Le 10 Sport says the former Athletic Bilbao defender now favours a move to Madrid. And it doesn't matter to the centre-half whether the move will be to Real Madrid or champions Atletico Madrid.
A confidant close to Laporte said: "He wants to come to Madrid and it doesn't matter if it's Real or Atlético.
"His new status as a Spain international prompted him to make the decision to sign for one of the teams in the capital."
Laporte has turned his back on France to commit to Spain as he features in the summer's Euros with La Roja.
This season with Manchester City, Laporte played 27 games, scoring twice. He featured for Spain in their opening Euro 2020 clash with Sweden, which finished 0-0. Now committed to Spain, Laporte has been capped through the levels of youth football by France. With the U21s, he had made 19 appearances.
- updated June 16
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