Fernandez has established a reputation as one of the most sought-after players in Europe after being named the Best Young Player at the 2022 World Cup with Argentina.
The 21-year-old scored one goal and set up one more to help La Albiceleste win their third World Cup title, having also starred for Benfica since arriving from River Plate in the summer.
Fernandez has three goals and five assists to boast in 25 games for Benfica, who have lost just one competitive match since the Argentina international made the move to Portugal.
Benfica are in a strong position when it comes to negotiations, as Fernandez is under contract until 2027 and supposedly possesses a mammoth €120m (£106.4m) release clause.
The youngster's price tag is unlikely to deter some of Europe's biggest names, with Real Madrid and Liverpool strongly linked with a January move, and Chelsea have also entered the race in recent days.
According to Metro, Chelsea have now struck an agreement with Fernandez on personal terms, and the midfielder has been convinced to join Graham Potter's side after holding informal talks.
It is now up to the powers-that-be to thrash out a price with Benfica, who are understood to be in talks with the Blues over a winter transfer but have nevertheless pointed to his £106m release clause.
However, Chelsea are supposedly hopeful that their agreement with Fernandez can help drive the fee down, while Liverpool and Manchester United have both been put off by his price tag.
Benfica returned to Primeira Liga action with a 3-0 loss to Braga on Friday - their first defeat of the season - and Fernandez played 89 minutes of that game despite the uncertainty surrounding his future.
President Rui Costa allegedly said that Fernandez would be allowed to leave if a club activated his release clause in January, but a statement from Benfica has since denied those reports.
"SL Benfica clarifies that at no time did the President of the Club, Rui Costa, utter the words that are being disseminated in Italy by DAZN. Sport Lisboa e Benfica reiterates its intention to count on the player Enzo Fernandez until the end of the season," Benfica said.
Chelsea have already confirmed the arrival of 20-year-old Ivorian striker David Datro Fofana from Molde and are on the verge of sealing a deal for 18-year-old Vasco da Gama midfielder Andrey Santos.
Co-owner Todd Boehly has been focusing on recruiting some of the globe's top young talents since taking over from Roman Abramovich, and Chelsea are understood to have identified four alternatives to Fernandez should a move fall through.
The Blues could lose both N'Golo Kante and Jorginho on free transfers next summer, but they are believed to have made progress in contract talks with the former.