Monchi oversaw the sale of Luiz this summer.
He told Sky Italia: "He is good, he is strong. For us last year he was a fundamental player, he played 90% of the total minutes.
"I am convinced that little by little he will find his best condition and will be an important player for Juventus."
The former Roma sports director was also asked about Daniele de Rossi's dismissal.
"Roma is a club that will remain in my heart forever, it was the first time I left Sevilla. It's a moment in my life that will remain forever, the first year we played the Champions League semi-final and that will remain forever. A beautiful place.
"No, I haven't (heard from De Rossi). I think it's a difficult situation but I don't know him and I can't comment on it. No one can question his love for Roma and he did a great job last year. But I can't say more."