The 22-year old performed brilliantly in the Championship for Peterborough United last season, scoring 13 goals after joining from League Two Dagenham & Redbridge.
Now he is set to move to the Premier League with suggestions that Palace and the Posh have agreed a fee even though the latter do not want him to depart.
"We don't want him to go. He is on a four-year contract but so many clubs are in for him that it is very difficult for us to stop a player from League One moving to the Premier League," Peterborough's director of football Barry Fry told the South London Press.
"It has got to be a good offer - then we'd reluctantly let him go to the Premier League.
"He has got four years left but we are honourable people. We keep our best players as long as we can but if we get a good offer then we will listen to it.
"We've done that with all our players. The difference here is that Dwight is on a much longer contract.
"He is the best player I've had - by 100 miles. Just look at his goals - right foot, left foot and head."