Attorneys for Nichols had asked that the entire DA's office be removed from the case following a ruling by the state Court of Criminal Appeals that upheld DA Bob Macy's disqualification.
But that ruling stopped short of also disqualifying his staff over allegations of professional misconduct.
In a one-paragraph order, the high court said the Court of Criminal Appeals "has exclusive jurisdiction in criminal cases" and dismissed Nichols' plea.
Jacobsen did not return a telephone call to his office.
Nichols, 45, was convicted in federal court and sentenced to life in prison for manslaughter and conspiracy in the 1995 bombing of the Alfred P. Murrah Federal Building that killed 168 people and injured more than 500.
He is awaiting trial in state court in Oklahoma on murder charges that could bring the death penalty.
In October, District Judge Ray Dean inder ordered Macy and his assistants off the case because of public comments by Macy that were deemed a "blatant violation of the rules of professional conduct."
Linder ruled that Macy had violated the rules of professional conduct as well as a gag order that prohibits anyone directly involved with the case from discussing it.
Among other public comments, in an interview with CBS News last April, Macy said: "I've sent several people to death row for killing one person. I certainly feel that death would be the appropriate punishment for killing 19 babies."
Nineteen children were among the bombing's 168 victims.
But the state Court of Criminal Appeals said the judge could not bar Macy's underlings from trying the case because the improper remarks involved mainly Macy, not his staff.
In a one-paragraph order, the Supreme Court said Monday that the Court of Criminal Appeals "has exclusive jurisdiction in criminal cases" and dismissed Nichols' plea.
Nichols was brought to Oklahoma City on Jan. 31, 2000, from Colorado, where he was serving a life prison sentence for his federal conviction on eight first-degree manslaughter counts and conspiracy charges.
No hearings have been scheduled in the case.
©MMI Viacom Internet Services Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report