Shrien Dewani's legal team applied to the High Court to try to get the case heard by the Supreme Court, the highest court in Britain.
"An application has been made to the court by Mr Dewani's lawyers in respect of the undertaking and for certification of points of law of general public importance and this will be listed for hearing in open court in due course," a spokesperson for the Judicial Office said.
Last month, the High Court ruled that Dewani could return to South Africa as long as the South African government makes a pledge over how long he would be kept in the country without trial.
He is being compulsorily detained at a clinic near Bristol under the Mental Health Act, suffering from severe depression and post-traumatic stress disorder.
Dewani is accused of organising the killing of his 28-year-old wife while the pair was on honeymoon in South Africa in November 2010.
While Dewani was released unharmed, Anni's body was found in the car the next day with injuries to her head and chest.
Dewani's lawyers say he will be willing to defend himself at a trial once he is fit to do so, but claim he is unfit to plead under English law.
In November 2012, South African national Xolile Mngeni was convicted of premeditated murder for shooting Anni and jailed for life. Prosecutors allege he was hired by Dewani to kill his wife, which the accused has denied.
Dewani's family have said that he remains committed to returning to South Africa "when his health would permit a full trial and when appropriate protections are in place for his health and safety".
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