Mr Trump, 74, plans to scythe through a raft of top officials if he secures a second term in the White House.
But Mr Wray, Ms Haspel and Mr Esper are understood to be the priorities because they are not trusted by the president's top team.
He would have sacked the trio already had it not been so close to election day, sources told Axios.
"The view of Haspel in the West Wing is that she still sees her job as manipulating people and outcomes, the way she must have when she was working assets in the field," one source told the publication.
"It's bred a lot of suspicion of her motives. "Since the beginning of DNI's push to declassify documents, and how strongly she feels about protecting sources connected to those materials, there have been rumblings around the agency that the director plans to depart the CIA regardless of who wins the election.”
Meanwhile, Mr Wray has been marked down for his failure to launch an investigation into Joe Biden over emails allegedly belonging to his son, Hunter, which the New York Post alleged were evidence of corruption.
The Daily Beast earlier this month reported that the president had already been mulling over sacking Mr Wray, But the perceived sleight on the Hunter Biden email story was thought to be the final straw.
Team Trump wanted to engineer a similar investigation to the one then-FBI director James Comey opened up during the 2016 race for the White House when he announced a fresh probe into Hilary Clinton's emails, the Washington Post reported.
Lastly, Mr Esper has reportedly fallen out of favour with the White House because he has been at odds with the president on how to deal with a wave of social unrest gripping the country following the police killing of black Americans.
Mr Esper publicly announced that there was no role for active military personnel in dealing with protests across the US that on occasion turned violent.
Mr Esper was also keen to distance himself from a controversial move by Mr Trump to clear out Lafayette Square for a photo opportunity at St John's church - the so-called church of the presidents.
Outside a place of God, the president held up a Bible to the cameras as he posed for photos. Just minutes earlier, law enforcement had used tear gas to disperse demonstrators from the area.
The moved was condemned by religious leaders, who said the president’s behaviour was at odds with the values of love and tolerance inherent in Christianity.
“Let me be clear, the president just used a Bible, the most sacred text of the Judeo-Christian tradition, and one of the churches of my diocese, without permission, as a backdrop for a message antithetical to the teachings of Jesus,” said the Right Rev Mariann Budde, the Episcopal bishop of Washington.
“We align ourselves with those seeking justice for the death of George Floyd and countless others. And I just can’t believe what my eyes have seen,” she added.