The 33-year-old, whose contract will expire this coming summer and has struggled to feature regularly for the Blues since coming back from a rib injury, is keeping his options open for the best possible deal.
The west London outfit could only offer him a one-year extension because of their existing policy covering players who are aged over 30.
Rivals Liverpool and MLS side New York Red Bulls are reported to be keen on acquiring the England international who still has much to offer on the pitch.
Chelsea are linked to be chasing Southampton starlet Luke Shaw, which may compel Cole to opt out, should a transfer materialise.
In any case, Blues manager Jose Mourinho will have the final say on whether the former Arsenal man can still stay at Stamford Bridge or not.