That silence comes as Trump's legal team and White House aides have advised the President not to tweet about the reports, two sources -- an administration official and a person familiar with the discussions -- told CNN.
White House advisers and others close to the President, including his attorneys, have urged Trump in recent days not to tweet about the revelation or subsequent reports on his son's meeting with the Russian lawyer, Natalia Veselnitskaya, those sources told CNN. Trump's senior adviser and son-in-law Jared Kushner and former Trump campaign chairman Paul Manafort also attended the meeting.
Trump advisers appeared less certain Tuesday afternoon that the President would continue to display restraint on Twitter after Trump Jr. released emails that showed he was willing to accept "information that would incriminate" Hillary Clinton from a "Russian government lawyer."
In the three days since the initial Times report -- amid subsequent reports from The Times that his son was promised damaging information on Hillary Clinton and told the information was part of a Russian government effort -- Trump has tweeted about his meeting with Russian President Vladimir Putin, retweeted a series of "Fox & Friends" clips and claimed he is "working hard to get the Olympics" to come to Los Angeles.
He even took to Twitter to defend his daughter, Ivanka, from criticism she faced for briefly holding her father's seat at the G20.
But when it came to the intensifying allegations against Trump Jr., the President has so far remained mum. And Trump is slated to again remain behind closed doors on Tuesday, his third consecutive day without any public appearances.
Trump's attorneys and advisers have often urged him not to tweet about reports concerning the federal investigation into contacts between Trump campaign associates and Russia, a probe that has since widened to look at whether Trump interfered with that investigation by firing FBI Director James Comey.
Trump has rarely heeded that advice in the past -- taking to his favorite social medium to push back on reports about his campaign associates and Moscow and the testimony of his former FBI director, for instance.
The White House in recent weeks has, however, sought to put more distance between the administration and the investigations into election meddling and the subsequent fallout.
White House spokespeople have offered little comment on the string of Russia-related allegations, instead directing reporters to the President's team of attorneys or the attorneys of the individuals involved in the latest reports.
The President, too, who has often been distracted and unnerved by the seemingly ceaseless allegations -- has been urged to keep his fighting instincts in check and to distance himself from reports and the investigations swirling around his administration, his former campaign associates, and now his family.
But even as Trump has kept his silence during now the third straight day that has been overtaken by allegations against his son, neither Trump advisers nor White House officials could express any confidence that Trump would heed their advice going forward.
Trump himself has made clear he has no plans to abandon his avid use of Twitter.
''It's my voice,'' Trump said of his Twitter account in an interview with The New York Times published Tuesday
. "They want to take away my voice ... They're not going to take away my social media.''