The 34-year-old has one year remaining on a two-year deal after he signed from Chelsea last summer.
He only made 11 Serie A appearances last season and has rarely featured in the club’s pre-season games under coach Rudi Garcia.
Cole was not included in the squad for Roma’s 6-4 friendly win over Sevilla on Friday night which saw Edin Dzeko score twice after sealing a season-long loan switch from Manchester City.
The members of the Roma squad were presented to supporters before the match at the Stadio Olimpico.
The former Chelsea and Arsenal left-back won 107 caps for England before retiring in 2014.