Van Zyl’s bid for the top job is helped by fifth-placed Cardiff being in a strong position to qualify for the URC play-offs.
They are one point behind the second-placed Stormers and 10 ahead of ninth-placed Connacht, but face a tough double-header in South Africa.
Cardiff take on Bulls in Pretoria on Friday (17:00 GMT) then Sharks in Durban seven days later, and have travelled with six of their eight-strong Wales contingent.
Only flanker Alex Mann and wing Josh Adams, who both started all five games in the Six Nations, have stayed at home and will not be summoned unless there are injury issues.
James Botham has travelled after he had an early introduction against Scotland and then started versus Ireland and Italy.
Centre Ben Thomas only started in round one against England, hooker Liam Belcher came off the bench at Twickenham and wing Mason Grady came on against the English and French.
The trio were released by Wales for game-time in the Six Nations’ fallow week, when they started against Leinster.
Tight-head props Keiron Assiratti and Sam Wainwright did not play in the championship.
