The State Press, a student-run newspaper published by the Arizona State University (ASU), reported that Volker, Executive director of the McCain Institute for International Leadership at the ASU, informed Secretary of State Mike Pompeo of his decision on Friday, Xinhua news agency reported.
Volker's post as special envoy since 2017 was a part-time, unpaid job to help resolve the armed conflict in eastern Ukraine, according to The New York Times.
He was mentioned in the whistleblower complaint released on Thursday that alleged, among others, that Trump had pressured Ukrainian President Volodymyr Zelensky in a phone call on July 25 "to initiate or continue an investigation into" the business dealings in Ukraine of Democratic presidential candidate Joe Biden and his son, Hunter.
Democratic lawmakers in the US House of Representative on Tuesday launched a formal impeachment inquiry into Trump, asking the State Department to depose five officials, including Volker.
The chairmen of three House committees investigating the Trump-Ukraine controversy requested that Volker's deposition take place on October 3, according to a letter they sent to Pompeo on Thursday.
Along with that letter, House Foreign Affairs Committee Chairman Eliot Engel, in consultation with House Intelligence Committee Chairman Adam Schiff and House Oversight Committee Chairman Elijah Cummings, also sent Pompeo a subpoena, asking the top US diplomat to "produce the documents" related to Trump's interactions with Ukraine by October 4.
Trump has denied any wrongdoing and dismissed the impeachment proceedings as a "hoax" and "another witch-hunt".
( With inputs from IANS )