It was confirmed today that Dewani will apply to the High Court in London in an attempt to have the case heard by the higher Supreme Court.
Dewani, 33, who is compulsorily detained in hospital under mental health legislation, is accused of ordering the killing of his 28-year-old wife Anni on their honeymoon in Cape Town in November 2010.
The South African government has given the required assurances on how long Dewani will be kept in the country without trial if he continues to suffer mental health problems, clearing the way for him to be sent there.
A panel of High Court judges ruled last month that it would not be "unjust and oppressive" to extradite Dewani, despite his illness, if the necessary undertaking was given by South African authorities.
Dewani denies any involvement in the killing of his Swedish-born wife, who was shot as the taxi the couple were travelling in was apparently carjacked.
A South African man, Xolile Mngeni, was jailed for life for the murder in December 2012. Two other men jailed over the killing allege that Dewani ordered the hit.