The committee canceled the hearing, which focused on the implications of the closure for US taxpayers, according to Neal, a consultant with Mnuchin on Wednesday.
A person familiar with the conversation between Mnuchin and Neal confirmed that the two men had spoken on the phone and had had a productive talk about the Chairman's concerns about the closure of the government and its impact on taxpayers.
During the call, Mnuchin expressed his willingness to appear before the committee.
CNN turned to the Ministry of Finance to comment.
Neal sent his request to Mnuchin last Wednesday, but did not release it until the next day, when President Donald Trump canceled entry to military aircraft for a convention trip to Afghanistan led by House Speaker Nancy Pelosi, citing the closure.
Faced with a possible policy setback due to delays in processing reimbursements, the Agency undertook to pay tax refunds and to lift a long-standing policy that reimbursements from individuals and businesses would not be paid in the event of a government deadlock.
"said Russell Vought, acting director of the Office of Management and Budget, to reporters on January 7. He added that the Trump administration is working to make the closure "as painless as possible, in accordance with the law."  A senior official told CNN at the time that the amendment was approved by an IRS memo from 2011, arguing that tax refunds can be paid out during a standstill.
More than 46,000 people, or about 57% of the IRS's workforce, have been driven for shutting down. The tax submission period starts on Monday.
The National Treasury Employees Union, which represents some 70,000 IRS workers across the country, said last Tuesday that the executive could not force more and more employees to appear in exchange for an IOU
"There is no doubt that the IRS has to prepare for the 2019 registration season, which starts on January 28, and the IRS staff want to work, "union president Tony Reardon said in a statement. "But the hard, cold reality is that they've already missed a paycheck and will soon be asked to work for free as long as the shutdown continues."