Swansea City are willing to sell Bafetimbi Gomis this month.
The London Evening Standard says Palace may have to pay up to £10million to sign Bafetimbi Gomis from Swansea.
The France international forward is a top target for Alan Pardew as he seeks to make the improvement to Palace's squad that will enable them to stay in the Premier League.
Even though Swansea sold Wilfried Bony to Manchester City for £28million this week, it is thought they would be open to offers for Gomis, although that will be conditional on their ability to line up a suitable replacement.