A British judge had rejected an appeal by the 33-year-old last month against being extradited to South Africa to stand trial for the murder of Anni Dewani.
Dewani's lawyers have now lodged an application at the high court here for judges to certify that a previous ruling made in the case raised "a point of law of general public importance" for consideration by the highest court in Britain.
The Bristol-based businessman, who has been in hospital due to mental health issues, is accused of plotting to kill his 28-year-old Indo-Swedish wife, who was shot in the head on the outskirts of Cape Town in November 2010.
Judge Riddle had previously given the go-ahead to Dewani's extradition in 2011 but had to reconsider the position after two senior High Court judges - Sir John Thomas, president of the Queen's Bench Division, and Justice Ouseley - allowed an appeal in March last year.
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They were told Dewani had depression and post-traumatic stress disorder (PTSD) and said it would be "unjust and oppressive" to remove him until he recovered.
They have claimed at various hearings that Dewani is willing to defend himself at a trial in South Africa once he is fit to do so.
So far three men have been convicted over Anni Dewani's death.
Last year, South African Xolile Mngeni was convicted of premeditated murder for shooting her.
Prosecutors claimed that he was a hitman hired by Dewani to kill his wife, something that Dewani has consistently denied.
Taxi driver Zola Tongo was jailed for 18 years after he admitted his part in the killing, and another accomplice, Mziwamadoda Qwabe, also pleaded guilty to murder and was handed a 25-year prison sentence.