The England centre-back spent 19 years at Chelsea after joining the club aged eight before leaving in the summer for Como, where he is enjoying a new challenge under former Arsenal midfielder Cesc Fabregas.
Chalobah remains in contact with Silva, who he has admired since his school days and studied closely during their time together in west London.
"Thiago has been a person I have always looked up to," Chalobah said.
"All the time when I was in school I used to watch YouTube videos of him, compilations of his game, from the time he was at AC Milan. To finally play with him at Chelsea was amazing and another dream come true."
Chalobah explained that he would study Silva's recovery and defensive movements while they were teammates, with one particular lesson standing out.
"I'm always in contact with him. When he was at Chelsea, I used to study his recovery and how he performed and operated," he said.
"That's what I learned from him: the 'what if' situation. He always used to say: what if this happens or that happens?"
The relationship has continued despite Silva returning to Brazil with Fluminense.
Asked whether the 42-year-old still offers him advice, Chalobah replied: "Yes, definitely. We talk online a lot, on Instagram. Funnily enough, he was at the England-Spain game watching, so that was good."
Chalobah also reflected positively on his long association with Chelsea, where he came through the academy before establishing himself in the first team.
"I'm really happy with what I achieved. Everything has tested me. It is testament to my faith and how I've gone about things there," he said.
"Growing up at Chelsea, with what they did for me, and how they allowed me to get to the first team, I enjoyed every moment — the trophies I won, the big games I played in."
However, Chalobah believes the move to Como was the right time to experience something different.
"It's been amazing. I felt now was the right time to try something different and try something new."
He has also welcomed the tactical differences in Italy, describing playing abroad as an important experience for his career.
"The Premier League is very fast, very physical, but I think [Italy] is a bit more tactical," he said.