A host of Premier League clubs have shown interest in the 22-year-old winger including Palace, but he will not be sold on the cheap.
The report claims that Palace will have to pay £25m for Saint-Maximin who has represented France at the Under 21 level.
He is highly rated in France, and would be a very good signing for Palace. He would provide competition for Wilfried Zaha at Selhurst Park, and could be a long term replacement for the Ivory Coast winger as well.
Newcastle were keen on him before the departure of Rafa Benitez, while there have been interests from Everton and Watford as well.
According to a recent report from Get France Football News, Newcastle have already contacted the player, and that he is close to agreeing personal terms with the Magpies over a possible summer transfer.
He scored six goals and provided three assists in 34 Ligue 1 appearances last season for Nice.