Cole, 33, is a free agent after leaving Chelsea last month, and the former England left-back has been linked with a move to America and Australia as well as Serie A.
Frank Lampard is set to move to the United States to play for New York City next March, and could feature for Melbourne City on a short-term deal in the interim.
But Sky Sports News understands that Serie A side Roma are now in pole position to sign Cole.
Although Cole is yet to travel to Italy in regards to the proposed deal, it is understand that Cole's representatives were due to meet with Roma officials on Saturday evening.
Chelsea bid a fond farewell to their defensive stalwart in a statement which read: "We say goodbye to Ashley Cole, a player who contributed enormously to the highly successfully period in our history in which we were crowned champions of Europe and won the League and Cup double for the first time.
"His remarkably consistent high level of performance was always appreciated by the Chelsea support.
"He collected winners' medals for the Champions League, the Premier League, the Europa League, the League Cup, the Community Shield and the FA Cup four times, taking him to his all-time record seven wins in that competition's long history."
Ashley Cole retired immediately from international football in May after being left out of Roy Hodgson's World Cup squad for Brazil.