The chancellor is expected to set out a range of smaller tax rises in her Budget, after backing away from increasing income tax rates.
However, the government has not ruled out extending the freeze on income tax thresholds – the level people start paying tax or have to pay higher rates.
The freeze means any pay rise would see people paying more tax, with more people dragged into a higher tax band, or having to pay tax on their income for the first time.
Reeves has also said there will be a focus on cutting the cost-of-living, with the government announcing that rail fares in England will be frozen next year for the first time in decades.
Other priorities set out by the chancellor include reducing NHS waiting lists and the national debt.
Meanwhile, she is also expected to scrap the two-child benefit cap, a limit that means parents can only claim universal credit or tax credits for their first two children.
There has been pressure from Labour MPs to remove the cap, which was introduced under the Conservatives – a move that could cost more than £3bn, according to estimates by the Institute for Fiscal Studies think tank.
While she refused to confirm the cap would be scrapped, Alexander said tackling child poverty was “in the DNA of the Labour Party”.
“One of the defining elements of this government for me is about what we can do to ensure that children’s chances in life aren’t determined by the size of their parents’ bank balance,” she added.
The Conservatives have argued against removing the cap, with Stride telling the BBC it was “a matter of fairness” that parents who are on benefits should have to make the same choices about whether they can afford a bigger family as those who are not.
The shadow chancellor told Kuenssberg: “The big choice at this Budget now is does the chancellor have the backbone to control government spending, particularly in the area of welfare where some of those costs are spiralling out of control, take those tough choices and therefore not have to start putting up taxes again in areas that are going to damage the economy.”
However, Green Party leader Zack Polanski said scrapping the cap would be a “victory” and it was “outrageous that it’s taken the Labour government so long to do it”.
He called for the government to “tax the rich”, rather than hit “people out of work or working people who are working really hard while their wages aren’t going up”.
Labour MP John McDonnell, the former shadow chancellor, said he hoped Reeves would announce a “redistributive Budget”.
“That does mean that the heaviest weight should fall on the broadest shoulders,” he told The Westminster Hour on BBC Radio 4.
“That means tax rises for the wealthiest and for the corporations, and for those who are making massive profits at the moment.”
Asked about divisions within Labour, McDonnell said: “We can do what we want in terms of getting stuff through Parliament.
“Yet we seem to be hindered by a lack of direction and some elements of competence as well.”
