Luiz recently stated his desire to return to his first European club after holding talks with Vieira as his contract in North London nears its expiry.
Vieira has however revealed that the 33-year-old Brazil international is preparing to renew his contract with Mikel Arteta’s side, as Benfica cannot afford his current wages.
"I spoke to him again yesterday. We have a father-to-son relationship," the Benfica president told Record.
"He was in the car with his agent, preparing to renew his contract with Arsenal.
"He is someone who loves Benfica, but there is something else he is: he is a great professional and has to earn money.
"What he earns is unthinkable for Benfica to pay. If David Luiz comes to a day when he says 'I want to leave here', if he is 35 years old, in perfect condition, we will take David Luiz of course.
"If he came, it would have to be for a million, but as a father, I would say 'No, David, you’re not coming, don’t be crazy. You have to make money!'
"When the football is over, nobody goes after him. If he came today, he would have to come under these conditions, otherwise, he could not come."
Luiz only moved to North London from Chelsea last summer for a transfer fee of £8m, signing a one-year contract with the option to extend for a further year.
Despite Arsenal’s managerial position changing hands a number of times this season, Luiz has been fairly constant under Unai Emery, Freddie Ljungberg and current boss Mikel Arteta, racking up 32 appearances in all competitions and scoring two goals.
