Totti, 39, has spent his entire career at the Italian capital club while the 37-year-old Conti left Roma to join Cagliari in 1999.
"You're getting old... I've heard that you're training to become a coach... I'm playing two more years, so if you want me to play (for you), I'm coming," Totti said on Monday.
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Totti made his Serie A debut in 1992 and became Roma captain in 1998.
He has played 592 games in Italy's top flight, third on the all-time list behind AC Milan's Paolo Maldini (647) and Inter's Javier Zanetti (615).
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Totti returned to action in Roma's 1-1 draw against AC Milan on Saturday following a thigh injury that had kept him out of the team since late September.
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