The Prince was present at St Mary's today to watch the Blades take on Southampton as they look for their first win of the season.
And, speaking before kick-off, he said: "It has been a tough season so far but I'm optimistic we can turn things around.
"When you have to make a decision, you'd better make it right. I could say that Chris has earned the right to stay because he won us two promotions in the last three years, but that is not how I look at it.
"If we get relegated, I'm set to lose big money so the decision to keep Chris is simply because I think he is the best manager to take us out of the current situation.
"I believe in him, if he wasn't the manager of the team I would hire him now and if the worst comes to the worst and we are relegated, I believe he is the manager to take us back quickly."
Wilder led United out of League One in his first season as Blades boss, before dragging them into the Premier League after just two seasons in the Championship.
Last season, their first in the top flight in 12 years, the Blades defied pre-season predictions of instant relegation to finish ninth, after flirting with the European places before lockdown.
"As far as I know Chris wants to stay and we want him to stay,” the Prince added.
"This year has been tough but I still have hope. It's a long season, but we will stick with Chris no matter what.
“I talk to Chris all the time, I met with him Friday and we're always in contact. We discussed the situation of the team, the January window and a lot of things. I like to talk to him, I was here so I met him and we had a very good talk.”