The two clubs have been locked in negotiations and super-agent Jorge Mendes has been drafted in to represent Chelsea and secure their deal for the Argentina midfielder.
Chelsea want to pay the transfer fee for Fernandez in instalments and initially offered £37.3m in three yearly payments.
But Benfica have asked for more money in the first payment, with 25 per cent of the fee they receive for Fernandez due to his previous club River Plate.
The clubs are now closer to an agreement over a deal that would be a British transfer record.
Fernandez, 21, was one of the breakout stars at the World Cup and Chelsea want to secure his signing ahead of possible interest from Manchester United and Liverpool in the summer.
Chelsea want to stagger the transfer fee as they bid to stay in line with UEFA financial fair play rules.
After spending £273m in the summer, Chelsea are among four Premier League clubs on a UEFA financial watch list.
Chelsea have identified Fernandez, along with Jude Bellingham, as a player who could become a mainstay of their midfield for years to come.
The Blues are also closing in on a £35m deal to sign Monaco defender Benoit Badiashile, having already completed the signing of Molde striker David Datro Fofana and Vasco da Gama midfielder Andrey Santos.