The Folha de S.Paulo and Estado de S.Paulo newspapers, citing presidential aides, said Rousseff abandoned the proposal because it realized there was no time to win its approval in Congress where the 2016 budget must be presented by Monday.
The president's press office said it would not comment on the tax issue until Monday as Rousseff planned to continue discussing the budget with her ministers on Sunday.
The government was planning a bill reintroducing a 0.38 percent levy on financial transactions, known as CPMF, to raise an estimated 68 billion reais ($19 billion) a year in revenue.
Finance Minister Joaquim Levy said on Saturday the tax was needed to cope with Brazil's fiscal crunch in a recession. A senior government official told Reuters on Friday that Brazil would not reach its 2016 fiscal savings target unless the CPMF, was abolished by Congress in 2007, was reinstated.
But business leaders, opposition politicians and even her main coalition ally, the PMDB party led by Vice President Michel Temer, opposed the plan to revive the unpopular tax.
Both newspapers estimated that the shortfall in the 2016 budget at about 80 billion reais and, if additional revenues are not found, the fiscal savings target for next year of 0.7 percent of gross domestic product might have to be reduced.
The fiscal crunch in the middle of a severe recession has undermined investor confidence and put Brazil at risk of losing its prized investment-grade credit rating next year.