Chelsea face three important fixtures in eight days, with the Bantams' visit to Stamford Bridge followed by the Capital One Cup semi-final second leg against Liverpool.
There is then the small matter of a top of the Barclays Premier League clash with Manchester City, but Mourinho is first and foremost focused on advancing to the fifth round of the FA Cup.
Mourinho, whose side play Paris St Germain in the last 16 of the Champions League next month, wants to be in contention on all fronts, even though cup runs are detrimental to Chelsea's ambitions of a first Premier League title in five years.
The Blues boss said: "To help the title race, the best thing is to lose against Bradford and to lose against Liverpool and to lose against Paris St Germain and to play only Premier League until the end of the season.
"But not with us
Not with our mentality, not with our way of thinking about our job, not with Chelsea DNA.
"The other day, a coach of a big team was knocked out of the cup and he was saying 'good, very good, this is perfect for us, now we can focus on the other competitions'.
"If I lose against Bradford I don't say that
I say it's a disgrace."
Mourinho, who believes fixture congestion means a quadruple is "almost impossible", would rather chase victory in every competition and fall short than not try at all.
"I prefer it very, very difficult, and congested, and lots of matches, and risk of losing everything," he added.
"But I can't choose matches, I can't choose competitions
"When we lose, we lose
But we want to win."
Chelsea's desire was evident at Liverpool.
Mourinho denied knowledge of a tunnel altercation between the indomitable Diego Costa and Liverpool's Jordan Henderson following the 1-1 first leg draw at Anfield, which reportedly followed on from a heated on-field exchange.
"I have no idea about what happened," Mourinho said.
"I think I was the first one to leave (the touchline)
It was too cold to stay outside."
Following the Anfield contest, Mourinho again called for Stamford Bridge to create some noise after saying in November he sometimes felt home matches were played in front of an "empty stadium".
Mourinho has also spoken of his dislike of a Chelsea fans' song about Liverpool captain Steven Gerrard, a player he once tried to sign and whose slip against the Blues last term may have denied the Reds a first championship in 24 years.
"Unless he comes to some club on loan (from Los Angeles Galaxy), the last time that Chelsea plays against Liverpool with Steven Gerrard is now in the Capital One Cup, is the game in the Premier League (in May), and - who knows? - also in the FA Cup," Mourinho said.
"So this will be the last two or three times that Chelsea play against Liverpool with Steven Gerrard.
"And I feel he was a fantastic 'enemy' - I don't like the word - a fantastic football opponent and I respect him a lot.
"When war has finished there are no enemies any more.
"I'm not trying to do something that Chelsea fans dislike or something to try to make them happy.
"I don't even think about it
I just speak by feeling, by emotion."
Source : PA