The Blues are one of a number of top European clubs who have entered the race to sign Fernandez along with the likes of Liverpool, Manchester United and Real Madrid.
Benfica president Rui Costa recently confirmed that the Portuguese giants will only sell the 21-year-old - who arrived at the club from River Plate in the summer - if his €120m (£106.2m) release clause is activated.
"We will sell Enzo Fernandez in January only for the €120m clause," Costa told reporters. "We would not like to sell Enzo Fernandez in January, but we are willing to satisfy the boy in the event of an offer of €120m."
Chelsea are understood to have stepped up their interest in Fernandez, who was named Young Player of the Tournament at the 2022 World Cup, and a recent report claims that the Blues have reached an agreement with the midfielder over personal terms.
Chelsea are now set to negotiate a transfer fee with Benfica, but should they fail to strike a deal with the Portuguese club, The Times reports that Graham Potter will consider raiding his former club Brighton for Mac Allister.
The 24-year-old - who starred alongside Fernandez for World Cup winners Argentina in Qatar - is said to be on a list of alternatives drawn up by Chelsea and is regarded as a more affordable option heading into the New Year.
Chelsea could face stern competition for Mac Allister's signature, though, as fellow Premier League sides Man United, Arsenal and Tottenham Hotspur have also been credited with an interest in the midfielder, as have Serie A giants Juventus.
Prior to representing Argentina at the World Cup, Mac Allister made a bright start to the 2022-23 campaign with Brighton, scoring five goals in 14 Premier League appearances under Potter and Roberto De Zerbi.
Brighton CEO Paul Barber recently confirmed that the club are in talks with Mac Allister over extending his contract, which expires in June 2025, but he has also admitted that he expects a number of teams will register their interest in the midfielder in the New Year.
"As we've always said, when players do well, when their profile increases, there's always going to be interest in them," Barber told talkSPORT.
"And this will be no different, Alexis is no different, there was interest in him before the World Cup and I'm sure there will be more interest in him afterwards.
"All we can do in situations where you've got a great asset is to try and protect yourself as best as possible. We've done that with several of our players and staff over the last several years, and that's all you can do in these situations.
"We hope Alexis will continue to be playing for us for some time to come."
Mac Allister was granted two weeks off by Brighton to celebrate Argentina's World Cup success and the midfielder is expected to return to first-team action at the beginning of January.