Benitez is out of contract next summer.
And supporters fear that the 58-year-old, frustrated at a lack of backing in the transfer market, will leave the club when his deal expires.
Benitez was forced to sell to buy in the summer after refusing to sign a new contract at St James’s Park.
Speaking in early August, Benitez said “everything” was wrong behind the scenes at the club, which is bottom of the Premier League and without a win this season.
However, United’s manager – who briefly met owner Mike Ashley after last weekend’s defeat to Brighton and Hove Albion – has not ruled out a longer stay on Tyneside.
“We still have plenty of time to talk about the future,” said Benitez, whose side take on Southampton at the St Mary’s Stadium this afternoon.
“The main thing is to be sure we do what we have to now, on the pitch, and then after we go to January and hopefully we can do things right. If so, we have more chance to survive.
“Last year, we were at the bottom and we did things right in January. We finished 10th. So that’s an example for this year.”
Asked if he could stay if the club does things “right” in January’s transfer window, Benitez said: “Yes, I’m happy here.”
Benitez doesn’t believe the uncertainty over his future is an issue for his players.
“I don’t think so,” said Benitez. “They’re clever enough to know that the future is Southampton – we can only concentrate on things on the pitch. If you listen to everyone outside, you will not to be focused.
“The best thing you can do for your team, your fans, your club, is to concentrate on doing the right things, and not listen too much to what is around.”
Benitez wouldn’t be drawn on what he discussed with Ashley, who has attended the club’s last four games.
“It was a normal meeting,” said Benitez.
“The good thing is he is coming to games now to watch.
“I will not discuss with the media what was said.”
Asked if they spoke about the January window, Benitez said: “The main thing is to focus on Southampton, the next game, and then we will have plenty time to talk.
“The scouting department are working really hard. We have communication, and we’re working hard, but the main focus is this game.”
Meanwhile, fit-again striker Salomon Rondon is in Benitez’s squad for the Southampton game.
“He’s in the squad,” said Benitez. “If you consider we signed him as our main striker, we were missing him.
“Hopefully, he can stay fit for a while and increase the competition. That’s good for the team.”
Defender Ciaran Clark is also available after missing the Brighton game through injury.
Asked about injuries, Benitez said: “Much better, we have (Florian) Lejeune and (Jamie) Sterry still injured – everyone is available apart form these two.”