Francois van Zyl, for Dewani, said the defence intended making an application to Deputy Judge Jeanette Traverso on Wednesday, in terms of section 174 of the Criminal Procedure Act.
The defence would file its heads of argument on Wednesday and the State would file responding papers on Friday.
Traverso said the application would be heard on Monday.
Section 174 of the Criminal Procedure Act provides that if at the close of the prosecution's case, the court believes there is no evidence that the accused committed the offence, it may return a verdict of not guilty.
The State closed its case on Monday.
Van Zyl said it had been a long trial and the defence needed time to prepare its application as there were many facts it had to deal with.
Dewani is on trial for allegedly plotting with shuttle taxi driver Zola Tongo and others to kill his wife Anni while they were on honeymoon on Cape Town in November 2010.
He has pleaded not guilty to charges including kidnapping, murder and defeating the ends of justice.
He claims the couple was hijacked while Tongo drove them through Gugulethu in his minibus on Saturday, November 13, 2010.
He was released unharmed and Anni was driven away. She was found shot dead in the abandoned minibus in Khayelitsha the next morning.
The State alleges he conspired with others to stage the hijacking, for which he paid R15,000.
He maintains that Tongo helped him organise a surprise helicopter trip for Anni for R15,000.
Tongo is serving an 18-year jail term and Mziwamadoda Qwabe, a 25-year jail term. Xolile Mngeni was serving life in jail for firing the shot that killed Anni, but died in prison from a brain tumour on October 18.