The Bayern Munich defender will draw to an end his 13 year spell with the Bundesliga giants when his contract expires in June.
And his future has been the subject of a huge amount of speculation, with a number of big European clubs believed to be interested in snapping him up on a free transfer, including Chelsea and Liverpool.
However, according to Sky in Germany Alaba has decided he is only interested in a move to one of the two elite Spanish clubs.
The 28-year-old has already turned down a lucrative offer from Paris Saint-Germain, and it is believed he is determined to seal a dream La Liga transfer.
It is unclear whether either Real or Barcelona will be able to meet his £400,000-a-week demands, however, given the level of debt they are both currently facing.
Alaba has forged a reputation as one of the best defenders in the world during his career, and has won practically everything possible during his time in Munich, including nine Bundesliga titles, two Champions Leagues, six German Cups and two Club World Cups.
But he announced his desire for a new challenge on social media in February, posting: “I have made the decision to leave #FCBayern at the end of this season and try something new.
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“It obviously wasn’t an easy decision – I’ve been here for 13 years and the club means a lot to me… I haven’t decided where I’m going next.”
A final decision is not expected to be made until either April or May, but Bayern have already sealed a replacement for Alaba, with RB Leipzig’s Dayot Upamecano due to join them in July.