The Federal Reserve did not immediately return a CNBC phone call for comment.
At its two-day meeting set to end Wednesday afternoon, the Fed is expected to raise short-term interest rates for the fourth time in two years. The central bank has kept interest rates near historically low levels as the U.S. economy emerged from the Great Recession in the last decade.
During his campaign, Trump criticized Yellen for keeping rates low for political reasons and said he would likely replace her. Yellen’s term ends in February 2018.
Former Goldman Sachs president Cohn sat next to Yellen, across from Trump, during the roughly 15-minute conversation, the Journal said Tuesday.
A White House spokeswoman told CNBC in late April chatter about Cohn being Yellen’s eventual successor was “entirely speculation.”
Trump told the Journal in an interview earlier in April that he was undecided about renominating Yellen and that he does “like her” and “respect her.” He also said, “I do like a low-interest rate policy.”