Ghailani, the first Guantanamo detainee tried in a U.S. civilian court, was convicted by a federal jury in November 2010 on a single conspiracy count to destroy buildings and property in the 1998 bombings of the embassies in Kenya and Tanzania. He was acquitted on 284 other counts.
In January, Ghailani was sentenced to life in prison without chance for parole.
A total of 224 people, including a dozen Americans, died and thousands were hurt in the attacks.
Defense attorney Peter E. Quijano Wednesday said his client's conviction should be overturned because the man's two-year detention in a secret overseas jail run by the CIA denied him his right to a speedy trial, The New York Times reported Wednesday.
While being detained by the CIA, Ghailani was subjected to so-called enhanced interrogation techniques to gain information about terrorist plots, the Times said.
"We have never disputed the right of the executive or the government to question someone under those circumstances in the name of national security," Quijano said, but two years in CIA custody was excessive.
Prosecutor Michael Farbarz argued against the appeal Wednesday, saying interrogators obtained productive information from Ghailani while he was in custody.