A spokesman for Shanahan said the acting secretary "has recused himself for the duration of his service" at the Defense Department "from participating in matters in which the Boeing Company is a party", reports Defense News.
He added, "President Obama fired him, and essentially so did I".
Mattis announced on December 20 that he was stepping down, but would stay on the job until the end of February.
Acrimony between Trump and prominent former military leaders has spilled into the open in the wake of Mattis' resignation. "And China is a major focus", the official said about Shanahan's China remark.
By focusing on China as opposed to operations in Syria or Afghanistan, Shanahan is possibly seeking an issue where Trump's views more closely reflect those espoused by the Pentagon's National Defense Strategy.
Appearing at Mr. Trump's side during Wednesday's Cabinet meeting at the White House on Wednesday, Mr. Shanahan said the Army Corps of Engineers was "dialed in" to help construct additional parts of Mr. Trump's Mexico border wall and that the Pentagon was exploring how to strengthen its support of the Department of Homeland Security's drive to curb illegal immigration.
"We're talking about sand and death". He has also not commented on planning for a dramatic drawdown in Afghanistan. But other officials have described him as a driving force behind the Pentagon's toughening stance toward Beijing, which includes branding China as a strategic competitor in the 2018 National Defense Strategy.
Trump suggested that Shanahan, who took over as acting defense secretary when Mattis ended his tenure Monday, agrees with him on this.
Acting US Defense Secretary Patrick Shanahan began his first full day at the helm of the Pentagon on Wednesday with an urgent list of geopolitical to-dos, including the US withdrawal from Syria.
Shanahan, who had served as deputy to Mattis since July 2017, is a career business executive with no prior government or military experience.
Relations between the world's two largest economies have plumbed new depths under Trump, with a trade war and disagreements over Taiwan and the South China Sea.
During Shanahan's tense Senate confirmation hearing in 2017, the committee's then-chairman, John McCain, voiced deep concern about giving the deputy job to an executive from one of the five corporations accounting for the lion's share of United States defense spending.