He previously led the Bianconeri to three consecutive league titles and managed the Italian national team between 2014 and 2016 before his arrival at Stamford Bridge.
Roma are currently under the guidance of former boss Claudio Ranieri, who penned a deal until the end of the current season after Eusebio Di Francesco was sacked following a run of poor form.
Conte has meanwhile also been linked with the top job at both Serie A rivals Inter and Bundesliga outfit Bayern Munich, but Totti has admitted he is keen to bring him to Rome, though he was careful to state that the club must give Ranieri his due too.
"We see that in recent weeks there is a lot of talking about Conte," Totti said to Sky Sport Italia. "We have Claudio Ranieri on the bench and we have to show respect.
"Every club would do crazy things for him. At the end of the season we'll decide if our coach will be Conte, Ranieri or somebody else. For now we are only thinking to qualify for the Champions League. It is not right to talk about coaches.
"I haven't met Antonio Conte. A change of coach will not depend on the fourth place or not.
"He is one of the best coaches in Europe. Any team would be crazy about him and the interest of Inter and Bayern Munich is the proof.
"With him on the bench there would be a winning [mentality]. It's inevitable."
Totti added Roma are hopeful of tying teenage midfielder Nicolo Zaniolo to a new contract following a promising season for the 19-year-old that has seen him win an international call-up.