In all seven of Argentina's games as they won the World Cup in Qatar, Fernandez emerged as a standout performer.
The 21-year-old, who transferred to Benfica from River Plate last year, was honoured as the Young Player of the Tournament in recognition of his achievements.
But several of Europe's top teams have taken notice of his performances, with Chelsea apparently in the lead.
Indeed, according to sources on Friday, Fernandez had already decided to join the Premier League team; Benfica's decision as to whether to accept a bid is now up in the air.
The rumours did not, however, deter Benfica coach Roger Schmidt from starting the midfielder in Benfica's first league match following the World Cup against Braga.
In response to a question on Fernandez during his pre-game press conference on Thursday, Schmidt said it was normal for a player to be intrigued by sizable offers.
"These young players sometimes have opportunities," he said. "It's not just Enzo, it's all the players.
" It's part of the football business. If they have opportunities, they have to make decisions. I can give them advice and recommendations.
"But I always respected the players' decisions, because they only have one career."