The 18-year-old, who burst onto the first-team scene at the age of just 16 at the beginning of last season, saw his release clause rise to a staggering £367m in the summer.
But his contract still expires in 2022 and the LaLiga giants are desperate not to lose him to a rival suitor and are thus keen to extend his deal, especially since he has become such a key member of Ronald Koeman's team this season.
Spanish outlet Marca report that talks between both parties started weeks ago and are 'on track' to be a success.
The 18-year-old winger is said to want a salary which now matches his importance in the first-team, despite a slight pay-rise in the summer.
However, any new deal will have to be ratified by the Barca board who come in amid the upcoming presidential elections in January.
The negotiations also come at a time when Barca are struggling financially due to the ramifications of the coronavirus crisis.
The Barca board, led by interim president Carles Tusquets, failed to agree pay-cuts with a number of first-team stars this week.
Manchester United were heavily linked with Fati in the summer, but suitors have now been warded off given his hefty release clause.
The player himself is currently recovering from injury after leaving hospital this week in a wheelchair five days after undergoing an operation on his knee, and is set to miss four months of action.
The 18-year-old wonderkid was withdrawn at half-time of the 5-2 win over Real Betis on November 7 due to a meniscus injury.
Fati went in to surgery on Monday and the club confirmed that he will not be available until March at the earliest as he recovers - he was captured on Spanish TV being lifted from a wheelchair into a taxi as he departed.
It is a setback for the teenager, who broke into the Spanish national team for the first time, scoring on his first international start to become the country's youngest ever goalscorer in September.