Fernandez, 21, won the award for young player of the tournament during the World CupChelsea are continuing talks with Benfica about signing Argentina midfielder Enzo Fernandez.
The 21-year-old World Cup winner has a release clause of about £106m, having joined the Portuguese club in August.
If Chelsea agreed to that amount it would eclipse the existing record fee of £98m paid for Romelu Lukaku and add to the record total of about £270m spent by the new ownership last summer.
Discussions are ongoing about the size of the fee and structure of the deal.
Chelsea's interest in Fernandez continues a recent policy of buying young players with the hope their value will be maintained over the course of long contracts.
Under new chairman Todd Boehly, the club bought Aston Villa midfielder Carney Chukwuemeka, 19, for £20m in the summer and last month agreed a pre-contract agreement with 20-year-old Molde FK forward David Datro Fofana.
But paying more than £100m for the former River Plate player would be a huge outlay for Boehly, who is still involved in negotiations but has been helped by new technical director Christopher Vivell.
The move for Fernandez is being made with the contracts of 31-year-old midfielders Jorginho and N'Golo Kante coming to an end this season.
Kante has only made two appearances this season because of injury but while it is believed the France midfielder has a good chance of earning a new deal, the future of Italy's Jorginho is less clear.
Chelsea are eighth in the Premier League, seven points outside the Champions League places and with one win in their last five games in all competitions, while they are winless in their last five Premier League away matches.
Analysis - 'The complete skill set, but a bit rash'
Zach Lowy, Portuguese football podcaster and co-creator of 'Breaking the Lines'
It's hard to overestimate just how good he Fernandez has been for Benfica. He didn't have any break whatsoever this summer after arriving from Argentina and was quickly ushered into the starting line-up under the new manager Roger Schmidt.
The first time I saw Fernandez was Benfica's league opener against Arouca, when he scored just before half-time. I remember a feeling I rarely get when I watch players for the first time - that the game comes so naturally to him.
He really has the complete skill set. He's been playing in the double pivot with Florentino Luis, who has more of a defensive profile and he has that mix of a deep-lying playmaker and a box-to-box midfielder.
The one flaw he has is being a bit rash in his tackles; he can get himself booked early on so he might need to adjust that, but his biggest skillset is just how complete he is.
Benfica fans recognise that their club cannot afford to keep players of Fernandez's talent for a long period of time. The reason they bought Darwin Nunez was because they knew they would sell him and it's the same with Fernandez.
So Benfica are resigned to the fact they will lose these players but they also know their club will demand top dollar. Nunez being sold allowed them to improve the squad in the summer and it's a constant cycle that Benfica fans are resigned to.
