Benitez was appointed as replacement for Steve McClaren in March with a clause in his three-year contract allowing him to leave if Newcastle dropped out of the top flight.
The Spaniard has overseen just three defeats since taking over - recording two wins and four draws - but was unable to prevent Newcastle from slipping into the Championship, which was confirmed as Sunderland beat Everton 3-0 in midweek.
Benitez said this week that he was undecided on whether he would remain at St James' Park to manage Newcastle in the second tier.
"We fought hard and everybody, at all levels at the club, have put in a lot of effort to try and turn our situation around. But we were unable to save ourselves from relegation," Benitez said.
"There have been injuries, missed chances and some unlucky moments over the course of the season, but we cannot make excuses. We are talking about 10 months and 38 games where we should have got more points, but we didn't.
"We have made mistakes and if you are in the bottom three at the end of the season, that is where you deserve to be. The table does not lie.
"We have already started thinking about the future. I have had conversations with people at the top of the club and we have been talking about what we need to move forward, and we are working on that.
"I will need some time for reflection, to think about the last two months and what lies ahead. I am very happy here but it is a difficult decision to make and one which I need time to consider.
"It is not just about following your heart but being sure that I can lead this club back into the Premier League at the first time of asking.
"I do not want to take on this challenge without the conviction that I will do well for the club, the fans and everyone who will put their confidence and trust in me.
"What I can guarantee to you is that I am considering the option to stay, because the potential of the club, the fans, the staff and the people of Newcastle have been even more impressive than I ever imagined it would be.
"I have enjoyed working here, and my time at St James' Park has exceeded my expectations, even if we were ultimately achieve what we set out to do over the final 10 games."
