While the Democratic Alliance (DA) wants to resume its disciplinary hearing against Cape Town Mayor Patricia de Lille soon, there are no time frames for the length of time it will take to reconstitute a full panel, DA federal council chairperson James Selfe said on Monday.

"We want to proceed as quickly as possible and we know she does too. So we would like to appoint and get things going as quickly as possible," he said.

The panel lost a member last week when Pogiso Monchusi recused himself. De Lille's legal team presented arguments to have him and Sheila Camerer removed.

The chairperson has not yet responded to the call for Camerer's recusal.

De Lille is accused of contravening the DA's federal constitution, amid claims of misconduct.

After the indefinite adjournment on Thursday, De Lille lamented that the postponement was costly for her because she had to pay her lawyers.

Selfe said the party would like to resume proceedings as soon as possible, but that it was dependent on the parties' availability.

"Another member of the Federal Legal Commission (FLC) will be appointed and will have to familiarise themselves with the facts of the case. Then the hearing can continue," he said.

The FLC tries to choose someone who hasn't been involved in previous matters concerning the parties - in this case, De Lille and the City of Cape Town - and who is not from the province concerned, Selfe explained.

"With those two restrictions, the pool becomes quite small. If someone decides not to participate, it becomes more tricky still."

The chairperson of the three-person panel is always a qualified lawyer, Selfe said.

While the remaining two don't need to be legal professionals, it is preferred in "complicated cases like this one".