The Spaniard has a break clause in his contract should the Magpies be relegated.
The Magpies are currently fighting against relegation, as they sit 19th in the table and one point from safety, with just three games of the season remaining.
Things had looked bleak before Benitez’s arrival, with the Spaniard having managed to turn things around at the club and keep them in the race in recent weeks.
Unfortunately for them though, he has a break clause in his contract should the club be relegated, and Hartson says they are fighting to persuade Benitez to stay as well as against the drop.
“Newcastle are fighting on a couple of fronts,” he told talkSPORT.
“They’re fighting foremost for their Premier League survival and also if they can just manage to stay up they may well persuade Rafa Benitez. He’s a top four manager, tactically brilliant.”
It is certainly hard to see Benitez staying at St James’ Park should they drop into the Championship this season.
He has spent the majority of his career competing at the top end of divisions, and will surely be keen to return to at least a top six challenging team in future.
That kind of job may be hard to come by though, and perhaps the Magpies can convince him to stay and build in the North East even if they are relegated.