Ahmad Umar Ali, 23, insists an examination would prove that Saudi officials had extracted a confession about the assassination plot from him through torture.
Ali's lawyer filed a motion on Monday seeking "immediate access to medical, psychological and forensic experts to examine and evaluate Mr Abu Ali for evidence of torture".
The motion was filed at Ali's arraignment in US District Court, where he pleaded innocent to providing material support to terrorists and other charges. The six-count indictment handed down last month could result in up to 80 years in prison.
Prosecutors say Ali, a US citizen, joined al-Qaida while studying overseas in Saudi Arabia and that he discussed "numerous terrorist acts" with other al-Qaida members, including a plan in which he would either shoot President Bush or detonate a car bomb.
Other discussions included a September 11-style attack in which planes would be hijacked from Britain or Australia and flown to targets in the United States.
An FBI agent testified at a previous hearing that Ali had admitted his guilt multiple times in interviews with Saudi and American authorities.
But Ali's lawyers say the government's evidence was obtained through torture and beatings he endured while in Saudi custody. Ali has said he was whipped by Saudi authorities.
Prosecutors have denied that Ali was mistreated.
US District Judge Gerald Bruce Lee said he would hold a hearing on the defence's request, possibly as soon as Friday.