The Colombian was signed last summer on loan from AS Monaco after he had an underwhelming season on loan with Manchester United last term.
However, he has only managed to score one goal this season and his time at the club has been blighted by injuries - meaning he has made just 12 appearances in all competitions since his arrival, including only one appearance in the past six months.
The 30-year-old was hoping to have a chance to perform under incoming manager Antonio Conte from the start of next season but has reportedly been told he can try and find a new club.
The main obstacle over a possible move to Roma appears to be his wages - said to be around £100,000 per week - with the Serie A side said to be in discussions with Monaco to see if a deal can be reached.
After gaining such a great reputation for his prowess in front of goal for both FC Porto and Atletico Madrid - in particular when he tore apart Chelsea in the UEFA Super Cup in 2012 - it is disappointing he has not been able to replicate that kind of form in the Premier League.
That said he has had a serious knee injury in the mean time, and joining United shortly after recovering from that problem represented a massive gamble that simply has not paid off - as with his subsequent spell with Chelsea.