The Washington Post, citing two sources in an article published Tuesday, said special counsel Robert Mueller specifically wants to question Trump about "his decisions to oust national security adviser Michael Flynn and FBI Director James B. Comey" last year.
The Post also said Trump's legal team wants to have the president answer questions through a combination of an in-person interview and a written statement.
A spokesman for Mueller declined to comment when CNBC asked about the Post report. CNBC has requested comment from Jay Sekulow, a lawyer for Trump.
In addition to investigating Russian efforts to influence the outcome of the presidential election, Mueller is probing whether Trump or others tried to obstruct justice in the investigation.
Earlier Tuesday, the New York Times reported that Attorney General Jeff Sessions met with Mueller's investigators for several hours last week. Comey met with the special counsel's office in late 2017, according to NBC News.