Ivor Bell, 79, from Ramoan Gardens, west Belfast, denies two charges connected to the murder of the mother-of-ten.
The IRA kidnapped Mrs McConville from her home in Divis flats in 1972.
She became known as one of the "disappeared".
These were people who were abducted, murdered and buried at secret locations by republicans during the Northern Ireland Troubles.
Mr Bell did not appear at the pre-trial hearing at Belfast's Crown Court on Monday. His barrister told the judge:  "He suffers from dementia which has a cardiovascular cause and he wouldn't be able to properly follow the course of proceedings."
A prosecution lawyer suggested that he would commission a psychiatrist to examine the defendant. He also requested full access to Mr Bell's medical files.
The case was adjourned until 16 December.
Mr Bell faces two counts of soliciting Mrs McConville's murder, both of which he denies.
Mrs McConville's remains were found on Shelling Hill beach in County Louth by a member of the public in August 2003. Nobody has been convicted of her murder.
The case against Mr Bell is based on the content of tapes police secured from an oral history archive collated by Boston College in the United States.
A veteran republican accused of involvement in the murder of Jean McConville is suffering from dementia and could not participate fully in his own trial, a court has been told.