Sources familiar with the investigation and President Trump's legal team confirm that the special counsel's team, in a letter sent Friday, agreed to accept written answers from Trump on questions related to the Russia investigation.
Those familiar with Mr. Trump's legal team say the development is viewed as a positive one for the president, and a response will be given to Mueller no later than the close of business Wednesday.
Mueller and his team have reserved the right to seek answers to questions related to obstruction of justice in a deposition.
Even so, those familiar with Mr. Trump's legal team now consider it is now less likely that Mueller will seek to compel presidential testimony through a subpoena.
The New York Times first reported that the special counsel would accept some answers in writing from the president in its investigation into Russian meddling in the 2016 election.
Mr. Trump's legal team has not seen the questions from the special counsel. The understanding reached so far is that the president's lawyers and Mueller's team will reach a common understanding of the time required to provide legal answers, and that process will likely takes weeks -- not days.
There is some general sense among the Trump lawyers and Mueller's team that the process could reach its conclusion by the end of September, though this is not certain.
Jay Sekulow, counsel to the president, said: "We continue to maintain an ongoing dialogue with the Office of Special Counsel. We do not discuss the contents of those discussions."