However with a majority in the House of Representatives, a number of individuals have pledged to aggressively investigate Mr Trump, his close aides and family members.
In his role heading up the committee, Mr Schiff has the power to call witnesses to testify before Congress and the authority to subpoena documents.
“It is now alleged that the President of the United States directed Michael Cohen to lie under oath to Congress about these matters in an effort to impede the investigation and to cover up his business dealings with Russia,” he said in a statement.
“These allegations may prove unfounded, but, if true, they would constitute both the subornation of perjury as well as obstruction of justice.”
The chairman of the House Judiciary Committee, Jerrold Nadler, also said directing a subordinate to lie to Congress constituted a federal crime.
“The @HouseJudiciary Committee’s job is to get to the bottom of it, and we will do that work,” the congressman tweeted.
The president hit back at the claims on Friday, suggesting Cohen was “lying to reduce his jail time” after pleading guilty to tax crimes, bank fraud and campaign violations.