Cole left Chelsea last summer after his contract at the club ran down, before joining Italian side Roma for the new season.
However the former England left back is said to be struggling in the Italian capital with his situation unclear – he has been dropped for the last five games in a row.
Any move hinges on persuading Roma to help with wage contributions with Cole currently on an £80,000 a week contract, while Palace have a wage ceiling on £40,000.
The paper have claimed that the club moved for Cole prior to his move to Roma before Tony Pulis stepped down as manager, and with Neil Warnock identifying a left back as a priority in January they are prepared to attempt an audacious loan move.
If a deal were to be done it would be some story with the player having spent a year on loan at Selhurst Park before his breakthrough to the Arsenal first team.
The defender made a huge impression at the club in 2000 and had previously hinted in 2010 he would one day like to return to the club.
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