The Trump administration is leaning on the Internal Revenue Service to upend how undocumented immigrants can file their taxes, as officials discuss changes that could force people to tell the agency about their immigration status or disengage from the tax system entirely.

At the center of the deliberations between Trump administration officials and the I.R.S., described by three people familiar with them, are potential changes to a nine-digit code, called an individual taxpayer identification number or ITIN, that people without a Social Security number can use to file their taxes.

Currently, a relatively large pool of people can receive an ITIN to put on their tax returns. It includes people living abroad who owe U.S. taxes, some immigrants with legal status and those without it. The codes can also be used to open a bank account, apply for a credit card and, in some states, get a driver’s license.

The change under discussion would differentiate codes for undocumented immigrants from those of other people with ITINs, the people said. Such a shift could require people applying for the codes to explicitly reveal their immigration status to the I.R.S., potentially discouraging them from getting a code or filing their taxes at all.

The proposal to assign the codes to separate categories is an evolution of an earlier idea from the Trump administration to create a new question on tax returns directly asking people if they are living in the country illegally, the people said.

The precise goal of the Trump administration push is unclear. Tax information on file at the I.R.S. is closely controlled, and an administration effort last year to share the agency’s data about undocumented immigrants with Immigration and Customs Enforcement has been blocked in court.