The Blues failed in their attempts to sign the Argentina international earlier this month, but they have reignited their pursuit in recent days.
They had considered other midfield targets, including Everton's Amadou Onana and Brighton & Hove Albion's Moises Caicedo.
However, Onana indicated that he does not want to leave the Merseyside club in January, while Brighton reportedly rejected Chelsea's £55m offer for Caicedo, who has also been the subject of at least two bids from Arsenal.
With Brighton keen to keep hold of the Ecuador international, Chelsea have turned their attention back to Fernandez, who joined Benfica from River Plate last summer.
Benfica have been holding out for Fernandez's release clause of 120m euros (£105.6m), which if activated, would have to be paid in full.
While Chelsea are not set to offer the full amount, BBC sport is reporting that a bid of 120m euros (£105.6m) in instalments has been tabled.
If the offer is accepted it would break the British transfer record set by Jack Grealish's £100m transfer from Aston Villa to Manchester City in 2021.
However, the report states that it is currently unclear whether Benfica would be prepared to accept Chelsea's latest offer.
Journalist Fabrizio Romano has claimed that Chelsea co-owners Todd Boehly and Behadad Egbhali are working to get the deal over the line before the transfer window shuts on Tuesday.
Benfica president Rui Costa has previously expressed his desire to keep Fernandez, but he is expected to decide whether to accept Chelsea's offer.
Mykhaylo Mudryk, Benoit Badiashile, David Datro Fofana, Andrey Santos, Noni Madueke have all joined on permanent deals, while Joao Felix has arrived on loan.
Malo Gusto recently signed from Lyon in deal worth £26.3m, which will see the right-back return to the French club for the remainder of the season, and should Benfica agree to a transfer then Fernandez would become Chelsea's eighth signing of the January transfer window.
Fernandez recently won the Best Young Player award at the 2022 World Cup, featuring in all seven games and contributing with one goal and one assist for eventual winners Argentina.
Since joining Benfica last summer, he has scored four goals and registered seven assists in 29 competitive appearances for the club.