Tottenham defender appears glad to have chosen North London move.
Sanchez was making just his second start for the club since his club record move from Ajax last month.
Sanchez insisted he was happy to have moved to Tottenham.
He said: "There is a lot of speculation and you realise that when you least expect it. I repeat that I am happy here.
"I have great teammates and since I arrived I have been given the confidence to be important. I do not know what will happen in the future, but for now I am very calm in Tottenham."
Real may well have been interested, but failure to move for the young defender is their loss.
There is little chance of Spurs letting him go now if he has a strong season, and even though he lasted just one year at Ajax before moving on.
Sanchez will get a chance to test himself against Real later this year when the two teams meet in the Champions League group stages.