The striker, who has five goals in 13 Real games, is on loan from Manchester City until the end of the season.
"I have two months to go and the club will decide what they want to do - but of course I want to stay," he said.
"I just have to keep working hard every day in training.
"They brought me here to help with the run-in to the end of the season - and today I have done that well."
Madrid coach Jose Mourinho brought Adebayor to the Bernabeu because Gonzalo Higuain was out through injury.
The Argentine made his long-awaited return on Tuesday night, while Frenchman Karim Benzema is injured after hitting a run of fine form.
Adebayor has now scored 10 goals in as many games against Spurs - with eight of those coming while with former club Arsenal, Tottenham's north-London rivals.
"I am very happy when I play against Spurs as I always have a chance to score," the former Togo captain said.
"So now we have to concentrate on the second game to go through to the semi-finals."
The second leg of the match takes place on Wednesday, 13 April, with the winner meeting either Barcelona or Shakhtar Donetsk in the semi-finals.
Source: BBC Sport
Source: BBC Sport