It would take them a small step closer to glory in a competition they have won a record 11 times, but not since 2004, meaning only Ryan Giggs, Paul Scholes and Darren Fletcher have winners' medals, along with Robin van Persie, who was introduced as a late substitute when Arsenal beat United in the 2005 final.
"We want to try and have a go at this FA Cup," Ferguson said.
"We haven't had a run for a long time, two or three years, and we have had some bad draws.
"We're at home tonight and we have got to take advantage of that.
"If we get through, we have got another home tie so there's a big incentive for the club to make sure we get through."
Skipper Nemanja Vidic is expected to sit the game out after suffering concussion in Sunday's win over Liverpool. Jonny Evans continues to nurse a hamstring strain, while Ashley Young is kept out by a knee injury, even if Ferguson has confirmed the damage sustained in a collision with Daniel Agger at the weekend is not as bad as first feared.
"Young has got a dull knock, a little bit of a strain on the knee, but it's nothing serious," said Ferguson.
"I think he'll be back next week. Maybe not for Tottenham on Sunday but, the week after, he should be okay."
On the positive side, Wayne Rooney and Nani will return after their absences.
Rooney has not been seen since suffering a knee injury during training on Christmas Day, meaning he has not had chance to erase the memory of an awful performance at Swansea.
Since then Van Persie has added another six goals to his tally, Javier Hernandez, three, and Danny Welbeck picked up man-of-the-match honours against Liverpool.
Clearly then, Rooney cannot endure a sluggish return from injury, as has been the case on too many occasions for Ferguson's liking.
"Wayne coming back is good news," said Ferguson.
"He's been training for a week and looking good."
Nani has been out for over two months and with speculation about his future beyond the end of the season remaining intense, he also needs to make an impact following a brief break in Dubai.
"Nani came back from his spell abroad and is really looking very good," said Ferguson.
West Ham manager Sam Allardyce, meanwhile, says he would not entertain a bid for defender James Tomkins, who has been linked with Newcastle.
With James Collins out with a hamstring injury, Tomkins, Guy Demel and Winston Reid are the only front-line defenders available for tonight's match.
Although Tomkins has been linked with a move to the Magpies, Allardyce is keen to add to his defence, rather than weaken it.
"It's impossible," the Hammers boss said. "But I might have a problem keeping him if they bid £15million."
Allardyce's defensive options are such that he is hamstrung for Old Trafford, the first of four matches the Hammers still have to play this month, meaning squad rotation is a must.
"There's nobody else I can play," he said.
"There are some players in front of that who play regularly who I will change."
Carlton Cole is poised to start up front, where resources are also limited with Andy Carroll (knee) out and Marouane Chamakh ineligible due to the terms of his loan from Arsenal, while Allardyce is still assessing the best way to integrate Wellington Paulista.
Ricardo Vaz Te could be pushed further forward, with the Hammers potentially changing formation for the fixture.
The manager added: "I'm going to look at the squad, the system. I might tinkle with the system."