It has been widely predicted that Spaniard, who took over from the sacked Steve McClaren in March, could take advantage of a reported release clause in his three-year contract to pursue other options.
Yet on the eve of Newcastle's final game of the season at home to Tottenham Hotspur, Benitez offered hope to the north-east club's fans, who were impressed with his attempts to stave off relegation, that he could still be in charge next season.
Benitez said he had met with Newcastle managing director Lee Charnley, adding: "The meetings were quite positive. We will continue.
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"If I decide to come here it's because it's a massive club and we have the fans. I am flattered with them. There will be more meetings."
The 56-year-old, who won the Champions League with Liverpool, said he would make his decision in the next two weeks, adding: "If I'm here and discussing it, it's because there is a chance. We have to keep talking."
The track record of the former Real Madrid manager will ensure there are plenty of suitors but when asked if he had been approached by Everton, who sacked Roberto Martinez earlier this week, he said: "I haven't talked with anyone."
Benitez's comments follow club owner Mike Ashley's open letter to Newcastle fans on Friday after their five-year stint in the Premier League was ended with bitter rivals Sunderland's midweek defeat of Everton.
Ashley said Newcastle's campaign had been "bitterly disappointing" and that he sympathised with the fans.
"I want to assure you that the club will now be doing everything it can at all levels to try to ensure a swift return to its rightful place," Ashley added.
(Reporting by Ian Chadband; Editing by Ken Ferris)
