Cole is available on a free transfer after seeing out his contract at Upton Park earlier this summer.
The appearance of an England international on the free market has drawn attention from a number of clubs across Europe and America.
West Bromwich Albion have been credited with holding an interest in Cole, with Baggies boss Steve Clarke having worked with the player while assistant manager at Chelsea and West Ham.
Cole's representative, Saif Rubie, has admitted there is interest from the Premier League, Europe and MLS, and that the forward is looking at all of his options.
"There are offers for Carlton from the Premier League, but also interest from Europe and big interest from MLS," Rubie told Sky Sports.
"At this stage we are looking at the pros and cons of each offer professionally and financially as this is a very important next step in Carlton's career and the move has to be right for him.
"We hope we can make a decision on Carlton's future soon."