The Washington Post quoted unidentified sources as saying that a US official was made to sign a pledge to pay an invoice for the medical costs before being allowed to fly Warmbier back home from Pyongyang in 2017.
The envoy signed the pledge on instructions from President Donald Trump, according to the Post report.
It was unclear whether the bill was ever paid, the report said.
Warmbier, a University of Virginia student, was imprisoned after being accused of taking down a propaganda poster in his hotel during a tour trip to North Korea. He fell into a coma after apparently being tortured behind bars and died days after arriving back in the United States.
White House spokeswoman Sarah Sanders' only reaction to the report was: "We do not comment on hostage negotiations, which is why they have been so successful during this administration."
Trump has made rapprochement with North Korea one of his signature policies and he has held two summits with North Korean leader Kim Jong Un.
At their last meeting in Hanoi in February, Trump said he accepted Kim's claim not to have known what had happened to Warmbier in prison, despite the case being extraordinarily sensitive.
"I will take him at his word," Trump said.