Speaking hours after addressing the Labour Party conference, the Home Secretary insisted the Government must "fix the foundations" of the economy.
Ms Cooper's Home Office is one of the "unprotected" government departments which means Chancellor Rachel Reeves could target it to claw back cash in her upcoming Spending Review.
Yesterday, asked three times to rule out cuts, Ms Cooper dodged the questions.
She said: "One of the things we've been doing in the Home Office is identifying the savings we should be making from clearing the asylum backlog, dealing with the huge overspend, the billions of pounds that were being spent."
Asked again if her department could be forced to slash its own budgets, the Home Secretary said: "It's not for me to pre-empt the Spending Review.
"But what we are doing is making sure we can save money on things where the Conservatives have failed, but also investing to make sure we can get 13,000 police and PCSOs on the streets that we set out in the manifesto."
Pressed over police budgets, Ms Cooper said: "What I can say is we focused on, 'What are the missions for this Labour Government?'
"One of them is about getting neighbourhood police back on to our streets. You've heard the Chancellor and the Prime Minister say that we are not going to go back to austerity.
Disorder
"What we are going to have to do is fix the foundations and get growth in the economy. That is the best way of improving public services."
Ms Cooper said the riots in August should not "silence a serious debate" on immigration, but claimed the Conservatives were becoming "Right-wing wreckers".
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