The Argentina star played the full match as the South American outfit beat France 4-2 on penalties in the World Cup final on Sunday.
And according to Record, the Portuguese side knocked back the bid as they are hoping a club will pay Fernandez’ release clause of £105m – which would make it the sixth-most expensive deal of all time.
Club president Rui Costa is said to be determined not to lose him for less than nine figures – which will likely come as a blow to Liverpool and manager Jurgen Klopp, who are keen on the 21-year-old.
Despite the Reds’ interest, the £88m bid is understood to have come from another European heavyweight.
Although only a small number of clubs – perhaps Man United, Man City, Chelsea, Liverpool, Real Madrid and PSG – could afford the asking price, Wednesday’s bid was just £17m away.
Benfica could find it hard to keep him if that clause is activated, with the contract offer understood to significantly improve Fernandez’ financial standing beyond Benfica’s capabilities.
The playmaker only moved to the Estadio da Luz this summer from Argentine side River Plate and has only been capped ten times by his country.
However, his value has soared after several stellar World Cup showings in Qatar.