Benitez’s name was chanted by supporters throughout yesterday’s 5-1 win over Tottenham Hotspur.
The club was last week relegated from the Premier League – it finished the season 18th in the division – and fans are desperate for him to take charge in the Championship.
And Benitez, despite having a clause in his managerial contract allowing him to leave in the summer, is considering staying on Tyneside.
But the 56-year-old – who met United owner Mike Ashley for talks after the game – has made it clear that he will be guided by his head as well as his heart.
“I think it was a great atmosphere,” said Benitez, who started the season at Real Madrid.
“I was expecting the fans to be behind the team and supporting me, but it has been really good and amazing and really positive.
“I was open to talk, and now I am more open to talk. Hopefully, we will start analysing what is going on and what will be the future of Newcastle United and my future.”
There were chants of “Rafa Benitez, we want you to stay” and “Rafa is a Geordie” during the game and after the final whistle.
And the Spaniard says it would “not be easy” to walk away from the club’s passionate support.
“I said I was flattered, but I am really pleased with that and it’s not easy to leave a club like this,” said Benitez.
“So I will talk, I will analyse and I will try to do the best for me and what is the best for Newcastle United.
“You can put it one way or the other way – the best for Newcastle United or the best for me. If we go together, it has to be the best for both.”
Asked if the emotional show of support had made a difference, he added: “I said before that I was expecting a great atmosphere, but it has been amazing.
“Even more positive than I was expecting. We still have to sit down. I want the best for Newcastle United and the best for me. That’s simple.”
It was the first time Benitez – who last week held talks with managing director Lee Charnley – had met Ashley, who hadn’t been to a game all season.
Speaking after the match, Benitez said: “My agenda is to talk to Lee Charnley, but if he is around then it is much better.
“If not, we will have time it is not a problem. I have an appointment with Lee Charnley, so I will talk to him. If they want both to talk with me, it will be fine.”