Ashley Cole arrived in Rome on Monday to discuss personal terms with last season's Serie A runners-up.
Cole, 33, is now a free agent after his Chelsea contract expired and his agent, Jonathan Barnett, confirmed at the weekend that the former England international was considering several offers from foreign clubs.
Roma were among those strongly linked with the left-back, and the club tweeted a picture of him arriving in the Italian capital on Monday morning.
He could be the second new arrival at the Giallorossi in a matter of days with Salih Ucan undergoing a medical in the Eternal City over the weekend ahead of a move from Fenerbahce.
"I believe in myself and in my quality and I'm sure I'll be successful at Roma," Ucan, 20, told reporters in Turkey prior to taking a flight for the Italian capital on Sunday.
"I want to make the most of this opportunity and I think it's the right chance for me."
By his own admission, Ucan is set to sign a two-year contract with the Giallorossi, who are preparing for their return to the Champions League next season.
They have already signed Seydou Keita while Urby Emanuelson is expected to arrive on a free transfer from AC Milan.
Fiorentina's Juan Cuadrado is another target, but Medhi Benatia could leave with Manchester City and Barcelona both showing an interest in the Moroccan central defender, who has been valued at 61 million euros by the Serie A club.