A federal judge said yesterday that he wants to review John W. Hinckley Jr.'s mental competency to stand trial on charges that he attempted to assassinate President Reagan in the light of Hinckley's unsuccessful attempt to hang himself 10 days ago at the Army stockade at Ft. Meade.

U.S. District Judge Barrington D. Parker ordered prosecution and defense lawyers to submits reports to him by Dec. 7 stating their views on whether Hinckley is mentally competent to understand the charges against him and to assist in the preparation of his defense.

At Hinckley's arraignment last August, lawyers on both sides told Parker they agreed that Hinckley was able to stand trial. But Parker indicated yesterday that the issue must be resolved again in light of Hinckley's second attempt at suicide on Nov. 15. On the first occasion, he reportedly took an overdose of an aspirin substitute.

Assistant U.S. Attorney Roger M. Adelman told Parker yesterday that government doctors believe Hinckley suffered no serious impairment as a result of the second suicide attempt. Defense lawyer Vincent J. Fuller said he was not prepared yesterday to address the question of Hinckley's mental competency.

Parker rejected a defense request that Hinckley be transferred to St. Elizabeths Hospital, the District's institution for the mentally ill, after hearing government testimony that the U.S. Marshals Service, which has custody of Hinckley, could not guarantee his security there. Hinckley is scheduled to stand trial Jan. 4.

Parker said that Hinckley could receive psychiatric counseling limited to his suicide attempt, and other medical treatment that the Fort Meade medical staff considered necessary. Any additional treatment would have to be approved by the court.

During a four-hour hearing, Parker also heard testimony about available facilities at Ft. Meade where Hinckley could receive psychiatric treatment. Dr. John E. Kehoe, an Army psychiatrist who has seen Hinckley four times since the second suicide attempt, said that he was unsure if it was necessary to transfer Hinckley from the stockade to the hospital setting.

Fuller questioned Kehoe's conclusions, noting other testimony that Hinckley had refused to talk to Kehoe.

Defense lawyers plan to argue that Hinckley was insane at the time he shot Reagan and three other persons, and should not be held criminally responsible for his acts. The lawyers' request for comprehensive psychiatric treatment has aroused prosecution concerns that the defense lawyers are trying to get a determination before the trial that Hinckley is mentally ill.

Parker also told the prosecutors to submit a detailed statement to him by Dec. 16 on the factual evidence they plan to use at trial.