In an excerpt from Woodward's recently released book, Fear: Trump in the White House, the US leader made the remarks after securing the release of Aya Hijazi, an American Egyptian who was detained by Cairo for three years.
Woodward claimed that Trump was talking to then-White House legal adviser John Dowd about his negotiations with Sisi over Hijazi's release.
Trump reportedly told Dowd: "Remember who I'm talking to. The guy's a f***ing killer. This guy's a f***ing killer! I'm getting it done. He'll make you sweat on the phone.
The book then describes Trump as assuming a "deep grovelling voice" apparently intending to mimic Sisi - "Donald, I'm worried about this [Mueller] investigation. Are you going to be around? Suppose I need a favour, Donald?"
According to Woodward, Trump called Sisi's comments, which were apparently in reference to Robert Mueller's investigation into alleged Russian meddling in the 2016 elections, a "kick in the nuts".
Hijazi was released from jail in April 2017, after nearly three years of imprisonment on human trafficking charges, which were widely dismissed as bogus by human rights groups.
Weeks earlier, Trump had invited Sisi to the White House, something former President Barack Obama had never done, and described him as a "fantastic guy".
Less than a year later, when Sisi won Egypt's election with 97 percent of the vote, Trump expressed his "sincere congratulations" to Sisi in a phone call.
Erratic and uninformed
Woodward's book, which was released on Tuesday after a widely publicised buildup, paints a highly-critical picture of life inside the Oval Office, painting Trump's character as dangerously erratic and uninformed.
It also claimed that Trump wanted to assassinate Syrian President Bashar al-Assad after an alleged chemical attack last April.
The book quoted Trump as saying: "Let's f***ing kill him! Let's go in. Let's kill the f***ing lot of them".
On the eve of its release, Trump took to Twitter to denounce Woodward's accounts as works of "fiction".
Cairo and Washington have forged close ties under Trump after years of tension under the Obama administration.
Obama temporarily halted military aid to Egypt after the Sisi-led overthrow of Egypt's first freely elected president, Mohamed Morsi, a member of the Muslim Brotherhood, in 2013. His administration also repeatedly criticised the Egyptian government's crackdown on political opponents.
Since the July 2013 coup, a police crackdown against the Muslim Brotherhood - which maintains it is peaceful but has been designated by Egypt's government as a "terrorist" group - has left hundreds dead and tens of thousands in jail.
Last year, a UN investigation found that Egypt engages in the continuous persecution of women, human rights activists, and journalists.
Human rights groups estimate that at least 40,000 political prisoners have been detained by Sisi's government.