"[The] leave to appeal will be heard in the South Gauteng High Court [in Johannesburg] on Thursday," said DA MP James Selfe.
Neither the National Prosecuting Authority (NPA) nor presidential spokesperson Mac Maharaj could confirm this.
The North Gauteng High Court in Pretoria recently ruled that acting NPA head Nomgcobo Jiba should lodge a copy of the tapes with the registrar of the court within five working days.
This was in response to an application by the DA, which has been battling to obtain the tapes after the Supreme Court of Appeal ruled that the party had the right of access to them.
Transcripts from the tapes and other documents relate to a 2009 NPA decision to drop corruption charges against Zuma.
The North Gauteng High Court in Pretoria gave the NPA until Friday to come up with the tapes, but Zuma's legal team filed notice that he would seek leave to appeal against the court ruling.
In court papers, Zuma's lawyers listed several grounds for an appeal.
One was that the court had erred in not finding that the transcripts of the tapes were part of Zuma's representation and, therefore, did not have to be produced.
"The court [also] erred... in holding that the third respondent [Zuma] was obliged to factually demonstrate that he had an interest in the confidentiality of the 'transcripts'."
According to the application, the appeal could be heard by either a full Bench of the high court, or by the Supreme Court of Appeal.
On Monday, Selfe expressed confidence that Zuma's legal team would not have a solid argument.
"The DA is of the opinion that President Zuma’s legal team’s appeal would not hold water in court and that they are delaying the inevitable," he said.