Liverpool go into their biggest home game of the season on the back of four consecutive defeats in all competitions, their worst run of form for 22 years, and Benitez was booed during the 2-1 home defeat by Olympique Lyon in the Champions League on Tuesday.
Dalglish said Benitez, with Liverpool languishing in eighth place in the Premier League - seven points behind leaders United - is the man to put things right.
"There's no way Liverpool Football Club and the majority of people would want Rafa to go anywhere," Dalgish, widely regarded as the club's greatest player and back at Anfield as an ambassador and working with the Academy, told the club's website on Friday.
"Everyone within the upper echelons of this club has no doubt whatsoever about Rafa - I know that for a fact.
"Everybody at Liverpool knows Rafa is the right man to get the club through this. No-one is pumped up and panicking in any way, shape or form. Everyone is being as helpful and supportive as they possibly can be to the manager.
"Obviously, whether you're a manager or a player, you have to retain your confidence and belief in what you are doing. It's very important that everybody sticks together.
"The other vitally important thing is that you must never allow other people to drive wedges between you and through various parts of the football club."
Benitez, who will take charge of his 200th Premier League game for Liverpool on Sunday, hopes to have striker Fernando Torres back for Sunday's clash with the champions although Steven Gerrard looks like missing out through injury.
Despite an abysmal start to the season, he said it was important not to panic.
"It is very important when you play against the top sides to show character and belief. That is what we must do on Sunday against United," he said.
"The main thing going into these games is that you stay calm. You cannot afford to think too much about if you win or lose before you've even played the game. That doesn't help."
