A fee has reportedly yet to be agreed, but if the deal is concluded it will see Gosling renew acquaintance with Ian Holloway.
Holloway gave Gosling his professional debut for Plymouth Argyle seven years ago and, after a stop-start spell on Tyneside, the Palace boss will be looking to help revive his career.
"He has had his talks with Crystal Palace and everything is agreed," the player's agent David Hodgson was quoted by the paper as saying. "We are not privy to how far (the clubs) are apart.
"The most important thing is for Dan to play football again and when your old manager comes in for you, and it is for a Premier League team, what better place to go?
"Ian Holloway gave him his debut at 16 and helped him play for England's youth teams. Dan is going to join somebody who knows him inside out.
"Playing football is very, very important but finding the right glove to fit into is even more important.
"A permanent deal is the intention and all parties would be happy with that."
Gosling has made only one Premier League start during his time with Newcastle, having joined from Everton on a free transfer three years ago.