The dynamic midfielder looks set to leave the Magpies this summer following the club’s relegation to the Championship last term.
Sissoko’s stock has risen this summer following some superb performances for France at Euro 2016, where his country were beaten finalists.
It has been suggested that Newcastle want at least £35million for the 26-year-old, who has been linked with Real Madrid, Paris Saint-Germain and Manchester United already.
However, reports in France have now claimed that is it Palace who are pushing hardest to sign him.
Manager Alan Pardew worked with Sissoko during his time as Newcastle manager and it has been reported that the Palace boss wants a reunion.
A new centre-forward had appeared to be Pardew’s priority this summer – with Christian Benteke and Saido Berahino both linked with a move to Selhurst Park.
But Le10Sport reckon he could now be turning his attention to completing a deal for Sissoko in time for the start of the campaign.