The Super Hoops are set to sell for around £8m, and although the Tyneside club are keen to keep the 27-year-old, the player himself wants to play European football.
Liverpool and Tottenham are also in the battle, but Arsenal are said to be leading the way.
It is understood that the Gunners have been conversing with the former Marseille ace, and that personal terms have been agreed.
Remy netted 14 goals in 29 appearances for Newcastle last term, and is viewed as a good option to compete with Olivier Giroud for the main striking berth in the Londoners’ XI.
The versatile forward has also been compared to Arsenal icon Thierry Henry, due to his good technical ability and tendency to drift in from wide areas.
It is thought that a deal could be formalised before the World Cup starts.