The curt exchange came in the midst of French President Emmanuel Macron, who is making his first official state visit to the U.S. this week.
Asked if he plans to pardon Cohen, whose residence and office were raided by the FBI in April, Trump said it was a "stupid question."
Trump's response came amid a flurry of speculation about Cohen's future in light of the aggressive raids, which were reportedly sparked by a referral from special counsel Robert Mueller, who is investigating the links between Trump's campaign and Russia.
Trump also recently pardoned Lewis "Scooter" Libby, chief of staff for Vice President Dick Cheney, who was convicted of lying to investigators and obstructing justice in the infamous Valerie Plame scandal. Trump suggested in a later tweet that more pardons could be forthcoming.
The White House did not immediately respond to CNBC's request for comment on Trump's remark.
Cohen, as well as a lawyer for Trump, attended a Manhattan court hearing last week to argue that they should be the first to review the documents that were seized in the raids. Lawyers for both Trump and Cohen have argued that swaths of the materials should be protected by attorney-client confidentiality privileges.
Some of the seized materials are reportedly related to porn star Stormy Daniels, who is suing Trump and Cohen to void a contract she signed before the election barring her from discussing an alleged affair, as well as the infamous "Access Hollywood" tape in which Trump is heard making sexual and lewd remarks about women.
Cohen brokered Daniels' contract, and paid her $130,000 as part of the agreement, which was signed just a few weeks before the 2016 election.
Trump and Macron were slated to address reporters at the White House during a joint press conference later Tuesday morning as part of Macron's three-day visit to the U.S.