The 32-year-old midfielder is currently on loan at Rennes and his parent club Roma are looking to terminate his contract mutually.
The French club are thought to be keen on signing the player permanently and it will be interesting to see if Arsenal and Everton make their move to snap him up before that.
Arsenal could definitely use a quality defensive midfielder like Nzonzi and the Frenchman would be an upgrade on Mohammed Elneny.
The former Stoke City midfielder would add some much needed protection ahead of the Arsenal defence and he would help the attacking players operate with more freedom as well.
Similarly, Everton could use someone like him as well especially with Jean-Philippe Gbamin perennially injured.
Nzonzi is 32 and he has one year left on his contract with Roma. He is unlikely to be expensive and it could prove to be a quality short term investment for both Premier League clubs.
Nzonzi has done well in the Premier League before and he has the experience to settle in quickly and make an immediate impact.
On a bargain, a player like him should be a no brainer for both Everton and Arsenal.
Both teams have the means to pull off the signing and it remains to be seen where the Frenchman ends up.