Luiz has formed a good rapport with both his teammates and the club's supporters, and Terry has admitted that the Brazilian centre-back uses that to try to get the best out of everyone on the training ground.
The 32-year-old told The Guardian: "Naturally, big Pete [Cech] will get the armband and, hopefully, I have a few years left, but you look at David Luiz and he has done incredibly well this year.
"He has stepped into midfield and been pulled back in certain games. It must be difficult for a player to be pulled left, right and centre but he is capable of doing it.
"He has the personality of a leader. He pushes the lads. He is like that in training, demanding a lot from himself and the other players around him. It's good for the squad."
The former Benfica defender made his 100th appearance for the Blues during their 3-0 victory over Fulham on Wednesday.