The former Real Madrid boss was appointed at St James' Park back in March, replacing outgoing boss Steve McClaren.
Despite initially signing a three-year contract, a clause in Benitez's deal means he can walk away from the club if they are relegated from the Premier League.
Although the Magpies are unbeaten in their last five games, the disappointing 0-0 draw with Aston Villa has brought them to the brink of falling out of the top flight, sparking speculation as to what Benitez's next move will be come the end of the season.
Reports have already linked him with a move to Everton, but according to the Daily Mail Newcastle are confident of persuading Benitez to stay and help rebuild the club, with the manager having a change of heart in the last 48 hours.
It added that Benitez is reportedly overwhelmed by the support he has got from the Toon Army, and is now determined to help the team get back on its feet.