Asencio has been a revelation since making his debut for Real earlier this term.
AS says City offered €6m for Asencio over the summer, but the bid was immediately rejected by Real.
City had planned to buy and loan Asencio to Girona this term.
Meanwhile, Real coach Carlo Ancelotti has said of his young defender: “He has shown himself to be a reliable centre-back. He absolutely does not lack knowledge of the position. He is very well positioned, confident and motivated.
"He has contributed a lot in these four games. If one day I have to put him on the bench I have to think about it carefully...
“Yes, he has surprised me, especially the maturity he has, the calmness he shows in handling game situations. He is never worried, you never see him afraid, he is very confident. He has already passed the test of fire, he can be considered a player of our squad with all the merit, because he deserves it.”