"The American people need to know that we are following the law and we expect them to also -- even if it extends the process," the Texas Republican told CNN's Chris Cuomo Thursday on "New Day."
Rep. Mick Mulvaney, nominated to lead the Office of Management and Budget, admitted in a questionnaire sent to the Senate Budget Committee that he failed to pay more than $15,000 in payroll taxes for a household employee.
A portion of the questionnaire was provided by a congressional source to CNN Wednesday.
The South Carolina Republican, in the questionnaire provided to CNN, wrote: "Upon discovery of that shortfall, I paid the federal taxes." The relevant penalties and interest "are not yet determined," he added.
The New York Times first reported on the questionnaire Wednesday.
Sessions played down the idea that Mulvaney dodged his taxes.
"If they paid their taxes, even if they maybe found out someone was not honest with them, that's different from not paying their taxes," Sessions told Cuomo.
Trump's selection of nominees was top notch but comes with qualifications, he said.
"That doesn't mean every single person in the vetting process," Sessions said, adding that senators are also right to closely examine Rep. Tom Price, the President-elect's nominee to be secretary of Health and Human Services.
Financial disclosures revealed that Price invested in a medical device manufacturer a few days before he introduced a bill benefiting that company.
Democratic lawmakers want an investigation to determine if Price violated the law.
"You should ask the questions, he should be required to put it in writing, and you should be able to offer some rebuttal to that to make sure that's correct," Sessions said.
But Sessions also defended the character of the Georgia Republican.
"He's an above board, honest, straight-forward guy but every single issues must be vetted and looked at and I'm for that," he said.