According to Bloomberg, citing sources, Trump thinks he can demote Powell - who was appointed by the president in November 2017 - to board governor, although he is not planning to do so at the moment.
Trump reportedly asked White House officials earlier this year to explore options to replace Powell, according to Bloomberg.
The news comes on the heels of Powell's comment that he intends to serve his full four-year term despite Trump's continuing criticism of current Federal Reserve policy.
Last week, Trump said that the Federal Reserve maintains high-interest rates that put the dollar at a disadvantage against the euro and other global currencies.
On 4 June, Powell said that US central bank is monitoring the impact of global trade developments and is ready to take steps to alleviate any harm that ongoing tariff disputes might cause the economy.
Powell did not directly reference interest rates, but his comments were widely interpreted to mean that the Federal Reserve could adjust its monetary policy if the trade wars dampen economic growth.
Earlier in the day, the Federal Reserve Federal Open Market Committee (FOMC) said in a statement that it will maintain the US interest rate in the 2.25-2.5 percent range.
The FOMC explained that it views the sustained expansion of economic activity, strong labor market conditions, and inflation near its symmetric 2 percent objective as the most likely outcome, but noted that uncertainties about the outlook have increased.
In light of the uncertainties and muted inflation pressures, the FOMC said it will closely monitor the implications of incoming information for the economic outlook and will act appropriately to sustain expansion, with a strong labor market and inflation near the group's stated objective.
The Federal Reserve’s decision comes after European Central Bank President Mario Draghi signaled on Tuesday a possible interest rate cut for the euro area. Trump, in turn, accused Draghi of currency manipulation.
In June 2018, Trump announced 25 percent tariffs on $50 billion worth of Chinese imports in a bid to balance the trade deficit between the US and China. Since then the sides have exchanged several rounds of duties.
Powell has reportedly said that the US business community has repeatedly complained to Fed officials about the negative ramifications of Trump's tariffs.
In January, Powell said that he would not resign if Trump asks him to step down.