"We will have content for Boxing Day but we're not yet in a position to announce that. We need to secure it first," ESPNcricinfo quoted Lorgat as saying.
The CSA CEO also said that a Test match is preferred over other formats for the Boxing Day and New Year.
"First prize is a Test match. We would love Boxing Day and New Year to remain as Test content. I know in the past there have been one-day matches and there has been discussion internally to consider one-dayers, but personally I would love to see a Test match played," he said.
It is believed that India are most likely to begin their tour to South Africa with the New Year's Test on January 5 or 6 next year in Cape Town.
The Boxing Day Test, which has switched between Durban and Port Elizabeth in recent years, is fairly poorly attended. However, it still remains a popular television event.
And now, it looks like they can invite Zimbabwe for a one-off Test during that period. If that happens, Zimbabwe could make their first Test appearance in the country since 2005.
West Indies are the other team available during that period, unless CSA reach out to Test newcomers Afghanistan or Ireland.
Despite India's tight time frame, the CSA is confident the tour will not be reduced from its original itinerary, and hopes to be able to announce match dates soon.
With the New Year's Test traditionally being played at Newlands from January 2, the CSA is reportedly trying to convince the BCCI to play the first Test from January 4 in a bid to maximise gate money.
"Now they (CSA) are trying to fit in everything within a short window," the official said. (ANI)