The teenager, who turns 17 on Halloween, has been starting games alongside Antoine Griezmann and Luis Suarez, showing no signs of fear by hitting two goals in his first three appearances in La Liga.
However, it's not just the Cules who are eagerly observing the rise of the attacker.
Fati has not yet represented anyone at international level, but he has unsurprisingly attracted a few suitors. Goal takes a look at who he is eligible to play for.
Which national teams is Ansu Fati eligible for?
Fati is potentially eligible for a number of national teams. Born in the West African country of Guinea-Bissau, he is first eligible to represent that country.
However, he has been living in Spain since he was six years old, progressing through the youth ranks of Sevilla and Barcelona.
He was granted Spanish citizenship by royal decree thanks to his residency in Spain for 10 years and he is thus eligible to play for La Roja.
Indeed, the Spanish football association (RFEF) worked with the government to ensure that Fati's application for citizenship went smoothly.
He will now be eligible for inclusion in the country's Under-17 World Cup squad.
"People at the RFEF are working on that to get Ansu [to play for Spain] and it will be the player's decision," Spain coach Robert Moreno told Movistar. "The RFEF are working on having the best players."
As well as Guinea-Bissau and Spain, it has been reported that Fati is also potentially eligible to play for Portugal.
Guinea-Bissau, the country where Fati was born, is a former Portuguese territory and special arrangements are in place regarding the acquisition of Portuguese citizenship.
Porto star Danilo Pereira is an example of a footballer who was born in Guinea-Bissau but who opted to play for Portugal, but Pereira had also lived in the country from the age of five.
It is unclear whether or not Fati could be a beneficiary of similar arrangements.
Which national team will Ansu Fati play for?
Despite being born in Guinea-Bissau, it appears that Fati has chosen to declare for Spain at international level.
The highly-thought-of attacker has spent a longer period of his life in Spain than he did in Guinea-Bissau, so it is perhaps no surprise that he may feel strongly about his allegiance to Spain.
Indeed, he is expected to get his first taste of international football when he is included in Spain's squad for the U-17 World Cup.
However, even if Fati does represent Spain at youth level, he will still have the option to ultimately declare for Guinea-Bissau or, if it turns out that he can become a Portuguese citizen, Portugal.
Only a competitive senior international cap - such as an appearance in a World Cup qualifier or European Championship match - will bind a player to a particular national team.
Games at U17, U19 or U21 level are not binding, nor are non-competitive games such as friendly matches.
How to change national team
Under FIFA's national team eligibility rules, footballers are permitted to request one change of national association.
The rules allowing a change of association are laid out in Article 8 of the FIFA Statutes.
Players who wish to switch their national team need to write to FIFA formally requesting a change and their case is then considered by the Players Status Committee.
Since Fati is not changing national association and Spain is his first national team, he does not need to go through this process at this point.