Conte was linked to Roma before taking over at Inter and, ahead of a meeting between the two sides on Friday, revealed he held preliminary talks with the Giallorossi.
The move came in the off-season, before Conte knew of Inter's interest, but the former Chelsea boss decided the timing was not right.
Conte spoke to ex-Italy team-mate and Roma legend Francesco Totti about the position before Paulo Fonseca was appointed in June 2019.
Totti, who spent his entire playing career with Roma, was a director at the club until he resigned the same month as Fonseca was installed.
Conte said: "With Francesco, there is a long-standing friendship. He explained the situation to me and told me about the possibility of Roma.
"I made an assessment in a very calm manner and thought it was not the right time.
"At that moment, however, an offer from Inter was not there. There were no other teams. I made my evaluation and I decided to decline the proposal in a very respectful manner.
"I know it's a huge club, but it wasn't the time. Maybe in the future."
Conte has been impressed by the job Fonseca has done at Roma, who are fifth in the Serie A table and nine points behind leaders Inter.
"He is demonstrating his qualities after his time in Ukraine [with Shakhtar Donetsk]," Conte added.
"Here, you have to settle in, your opponents study you and prepare very well to stop you. He brought an idea and also used it in Serie A.
"Roma deserve compliments. They have a competitive squad made up of experienced players and very good talents.
"They are in a great moment of form. Roma have a maturity, strength and knowledge which will force us to show them respect."
Meanwhile, Roma has been boosted by the availability of striker Edin Dzeko for the match.
The 33-year-old Bosnia international had been struggling with a bout of flu but will be in the squad that travels to Milan for the clash at San Siro.
Fonseca said: "He missed the last couple of sessions but Edin trained with the group today – he's fit to play."