So far there is no indication whether the Blues’ offer, thought to include instalments, will be accepted.
But if the deal goes through, it would eclipse the £100m Manchester City paid Aston Villa for Jack Grealish in 2021.
Fernandez was named young player of the tournament during Argentina’s World Cup triumph in Qatar.
Benfica have previously accused Chelsea of trying to unsettle the midfielder, with the Portuguese side’s manager Roger Schmidt declaring their pursuit “closed”.
However, it is not thought the Premier League club would have made a fresh offer without being given some indication it might be accepted.
Fernandez only joined Benfica from Argentinian side River Plate in August, for a reported £10m, and has scored four goals in 29 appearances for the Primeira Liga side.
He scored once during the World Cup, netting Argentina’s second goal in their 2-0 group-stage win over Mexico.
Chelsea have signed Noni Madueke, Mykhailo Mudryk, David Datro Fofana, Andrey Santos, Benoit Badiashile and Malo Gusto on permanent deals in January and brought in Joao Felix on loan from Atletico Madrid.
It comes after a summer that saw them spend a Premier League record £270m – the second-highest summer spend by any club in the world after Real Madrid (£292m) in 2019.
Source: BBC