According to Sky Sports, Palace are desperate to bring in a new striker, and with the club yet to reach an agreement with Fiorentina over the transfer of Khouma Babacar the Eagles have now turned their attention towards Barnes.
Eagles manager Roy Hodgson has reportedly been given between £10m and £12m to spend this window, however Burnley are said to be reluctant to sell Barnes, who still has 18 months left on his contract.
Palace have already been busy in this window by already bringing in Erdal Rakip and Jaroslaw Jach. The club have also been in pursuit of Lille midfielder Ibrahim Amadou, with a three bids reportedly turned down already by the French club.
It seems very unlikely that Barnes would mover to Selhurst Park in this window, especially given that he is playing most weeks for a Burnley team that have overachieved so far this season. Hodgson may have to look elsewhere if he wants to bring in a striker this January, and with a new man up top their chances of safety would definitely increase.