Honeymoon murder suspect Shrien Dewani will continue to fight his battle to delay his extradition to South Africa, the British Press Association reported on Friday.
Dewani would apply to the High Court to try to get the case heard by the Supreme Court, the highest in the land.
"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 spokeswoman for the Judicial Office said.
A panel of High Court judges, headed by Lord Chief Justice Lord Thomas, ruled last month that it would not be "unjust and oppressive" to extradite Dewani, despite his illness, if an undertaking was given by South African authorities.
The South African government has given assurances on how long Dewani will be kept in the country without trial if he continues to suffer mental health problems, paving the way for him to be sent there.
Dewani, 33, from Bristol, has been fighting removal from the UK to face proceedings over wife Anni's death until he has recovered from mental health problems, including severe depression and post-traumatic stress disorder.
His lawyers have said at various hearings that he will be willing to defend himself at trial once he is fit to do so, but they say he is unfit to plead under English law and his "prognosis is not certain".
Dewani, who is compulsorily detained in hospital under the Mental Health Act, is accused of ordering the killing of his new wife Anni, 28, on their honeymoon.
The pair were kidnapped at gunpoint as they drove through the Gugulethu township in Cape Town in a taxi in November 2010. Dewani was released unharmed.
The next day the body of his wife Anni was found in the car. She had injuries to her head and chest.
South African Xolile Mngeni was later convicted of premeditated murder and jailed for life. Prosecutors allege he was hired by Dewani to kill his wife.
Dewani has always denied the accusation and has been fighting efforts to secure his extradition since it was first ordered by a senior district judge in 2011. –Sapa