The 24-year-old, who has been at Montpellier for five years, has been a top target for the Magpies ever since they sold Yohan Cabaye to Paris Saint-Germain last January.
The St James' Park outfit are believed to have had a £6.5m bid for Cabella rejected earlier this summer, but now seem to be closing in on their man after negotiating a £12m package for the playmaker.
On Friday, French media quoted Montpellier CEO Laurent Nicollin as saying: "We have a deal". Sky Sports News reports that the move is expected to completed before the end of the week.
Cabella, who was part of the Les Bleus squad that reached the quarter-finals of the World Cup this summer, scored 14 goals in 37 Ligue 1 games last season - his most prolific since debuting in 2009.