The 21-year-old has broadly agreed personal terms with Chelsea and even failed to turn up for Benfica training in a bid to force a move to Stamford Bridge.
Chelsea want to pay the transfer fee for Fernandez in three £37.5m instalments as they bid to stay in line with UEFA financial fair play rules.
After spending £273million in the summer, Chelsea are among four Premier League clubs on a UEFA financial watch list.
With their transfer activity being scrutinised, Chelsea want to structure a deal for Fernandez across three yearly payments.
Fernandez was one of the breakout stars at the World Cup and Chelsea have identified him, along with Jude Bellingham, as a player who could become a mainstay of their midfield for years to come.
After playing a key role in helping Argentina win the World Cup, Fernandez returned to Portugal and played for Benfica in their Primeira Liga game against Braga on December 30.
But he returned to Argentina without permission to celebrate New Year's Eve and has yet to return, missing training twice last week. He is expected to be punished by Benfica and believes he has played his last game for the club he joined from River Plate last summer.
All parties are keen to resolve negotiations by next week. Should talks collapse, that would leave Chelsea time to explore alternative targets like Brighton’s Alexis Mac Allister and Ajax’s Edson Alvarez.
Benfica are reluctant to receive any fee for Fernandez in instalments, given River Plate are due 25 per cent of the total transfer fee of his next move, but Chelsea are hopeful of reaching a compromise.
Chelsea are also closing in on a £35million deal to sign Monaco defender Benoit Badiashile, having already completed the signing of Molde striker David Datro Fofana for around £10m.
The Blues are also closing in on a deal to sign 18-year-old Vasco da Gama midfielder Andrey Santos.