The 33-year-old left-back, released by Chelsea this summer, has been in discussions with a number of foreign clubs via his representative.
Sky Sports learned last week that Cole’s most likely destination would be either MLS or Serie A, with Roma showing strong interest in the former England international and they are reportedly ready to offer him a two-year deal.
The defender, who announced his international retirement after being overlooked by Roy Hodgson for England’s ill-fated World Cup campaign, became a free agent along with Frank Lampard at the end of the season, after Chelsea opted not to renew their contracts.
Lampard told Sky Sports last week that he will also make a decision on his future imminently, with his most likely destination to be MLS side New York City after holding talks with the club over a move last month.
Cole signed for Chelsea in a controversial move from rivals Arsenal in 2006 for £5million and went on to play over 300 appearances for the club.
He lifted the Premier League under Jose Mourinho in 2010, before clinching the 2012 Champions League under Roberto Di Matteo, as well as the 2013 Europa League with Rafa Benitez, and five FA Cups.
Cole was a bit-part player last season however, following Mourinho's return to Stamford Bridge and he was deemed surplus to requirements by both his club and country at the end of the campaign.