United face a showdown with fellow League Cup semi-finalists Liverpool in the league at the weekend.
United cruised into the FA Cup fourth round on Saturday after registering an eighth consecutive win by crushing second-tier Reading 4-0 at Old Trafford.
They face a showdown with fellow League Cup semi-finalists Liverpool in the league at the weekend, but with a day out at Wembley only 180 minutes away, Mourinho does not want to take any chances.
"We play against Liverpool, a big match for us, but we want to be in the final," he said.
"So we are going to face this Hull match with everything we have, all the power we have, as we know it's two legs, but the second leg is away.
"If we can do something in the first leg that gives us the advantage, we will try to do that."
Mourinho made a number of changes for the visit of former United defender Jaap Stam's Reading and has revealed he will restore several first-team regulars for the visit of Hull.
"I play with the players that didn't play (against Reading)," said Mourinho, who won three League Cups over his two spells as Chelsea manager.
"I played with fresh players and I don't want to say anything about first-choice or second-choice, but we played with fresh players, the players who didn't play against West Ham.
"In the next match against Hull City we are going to play again with fresh players. So it's easy to know our team -- Zlatan (Ibrahimovic), (Paul) Pogba, (Ander) Herrera, (Antonio) Valencia."
Wayne Rooney equalled Bobby Charlton's United scoring record by netting his 249th goal for the club against Reading, but he is likely to drop to the bench against Hull.
Centre-back Marcos Rojo is a doubt after being withdrawn against Reading with a muscular problem.
With Eric Bailly having departed for the Africa Cup of Nations with Ivory Coast, it could leave Phil Jones and Chris Smalling as United's only fit senior centre-backs.
Marco Silva made a winning start to life as Hull head coach with a 2-0 victory over Swansea City in the FA Cup on Saturday and he will relish the prospect of tackling fellow Portuguese Mourinho.
"It is a fantastic moment for the club that we play Manchester United in a semi-final," Silva said.
The carrot of a potential final appearance against arch rivals United is sure to motivate Liverpool when they travel to Southampton on Wednesday for the first leg of their semi-final.
Having fielded Liverpool's youngest ever team in their 0-0 FA Cup draw at home to fourth-tier Plymouth Argyle on Sunday, manager Jurgen Klopp is also expected to revert to a full-strength team.
"That's only in a few days," said Klopp, whose side lost on penalties to Manchester City in last season's final.
"I have no idea (about fielding a more experienced line-up), but probably, yes. It's pretty likely."
Southampton are seeking to reach a first major final since their 1-0 loss to Arsenal in the deciding match of the FA Cup in 2003.
Claude Puel's side came within a whisker of reaching the FA Cup fourth round on Saturday, only for Steven Naismith's 92nd-minute header to earn Norwich City a 2-2 draw and take the tie to a replay.
Portuguese centre-back Jose Fonte, who has reportedly asked to leave the club, did not feature against Norwich and Puel refused to be drawn as to whether he would play against Liverpool.
"You can understand I cannot give an answer about this," said the Southampton manager.
"It is between Jose and the club and we will see in the future."
Tuesday (2000 GMT):
Manchester United v Hull City
Wednesday (1945 GMT):
Southampton v Liverpool