An excellent performance from Fernandez at the 2022 FIFA World Cup in Qatar, where he was named best young player of the tournament, has seen a number of suitors queue up for his signature.
Fernandez only joined Benfica from River Plate last summer and has made 25 appearances across all competitions, scoring three goals and providing four assists.
The 21-year-old has a release clause of £106m but Chelsea are only willing to pay the total fee in installments.
Chelsea's pursuit of Fernandez has reportedly unsettled the player, who took an unsanctioned trip back to Argentina to celebrate the new year, angering his club.
"We don't want to sell Enzo, neither I nor the president," Schmidt told reporters on Thursday.
"We all know he has a clause in his contract. If he wants to leave and if someone meets this clause, we can do nothing.
"There is a club that wants the player, that knows we don't want to sell, that tries to put the player on their side when they know that the only way to get him is to beat the clause.
"The situation is very clear. What that club is doing to try to sign Enzo is [showing] a lack of respect for Benfica."
"I cannot accept what they are doing. They try to drive the player crazy, pretending they're going to pay the clause and then say they want to negotiate.
"I think that's not the way for two clubs to have good relations."
"Enzo is a very good boy and a fantastic player. We like him very much and we want him to stay. But his situation is not easy," Schmidt explained.
"He played in a World Cup, was world champion and there's a lot of money on the table.
"A player can get confused when he thinks about it and I think it's a situation that everyone understands. He wasn't allowed to go to Argentina, he missed training and that's not acceptable. There will be consequences, I won't say what."
