United has struggled this season, collecting 10 points from its opening seven Premier League matches and being dumped out of the League Cup by second-tier Derby County.
It did, however, secure an emphatic 3-0 victory over Young Boys in its first Champions League group match.
Since then, reports of unrest with leading player Paul Pogba, which led to the Frenchman being demoted as vice-captain, have led to suggestions that Mourinho is losing his influence at Old Trafford.
But the Portuguese coach was in a confident mood on Monday and when asked at a news conference if he felt his job was on the line, he simply answered: “No, I don’t.”
Media reports following United’s 3-1 league defeat at West Ham United on Saturday linked former Real Madrid coach Zinedine Zidane with Mourinho’s job. Asked if he had spoken to the club’s executive vice-chairman Ed Woodward following Saturday’s loss, Mourinho gave a tetchy reply.
“That’s a private matter. I’m not asking you who did you speak with yesterday or this morning, who was your last phone call, that’s a private matter. I’m not going to answer it,” he said.
The West Ham defeat drew sharp criticism from defender Luke Shaw who said United needed to take responsibility for the “horrendous” result.
Mourinho said it was down to more than just the players to turn the situation around.
“The performance on the pitch is the consequence of many factors,” he said.
“Luke Shaw for example said ‘we players on the pitch have to give more’. I like that perspective but I don’t agree totally. Everyone at the club has a role to play. The kit man, the nutritionist. I have a role to play, everyone has a role to play.
“I think that some care more than others,” he added.
Tuesday’s match at Old Trafford could be a good opportunity for United to bounce back against a Valencia side which has one win in eight matches in all competitions this season, although that came against Real Sociedad on Saturday.
United go into the game depleted as Ashley Young picked up an injury during the loss at West Ham, while Marcos Rojo, Ander Herrera and Jesse Lingard are also sidelined. Midfielder Nemanja Matic said the West Ham defeat was one of his worst games for United.
“Everyone has a responsibility,” he said. “We have spoken between us and we know the situation is not good and we can do better. Everyone is trying to do more for the team. “Tomorrow is a great chance to do that against a big team. I expect everyone will give more and be more concentrated.”