There are increasing reports that Prime Minister John Vorster may announce this week that he is stepping down from his position as head of this country's white minority government because of illness.

Speculation that Vorster, 63, is seriously sick and might resign began in the English language press about a week ago. It took on added significance when the Afrikaans language newspapers, which are vehicle for government views, joined the discussion in the last few days.

"Our press is like Pravada," said one Afrikaner. "This speculation about government officials does not go on unless they are sure about what is going to happen or they are told to prepare the people for some change."

A report yesterday by a journalist regarded as extremely close to Vorster said the prime minister would announce his decision at Tuesday's Cabinet meeting.

If Vorster does announce his resignation, political observers believe he will make himself available for the ceremonial post of president, left vacant last month by the death of Nicolaas Diederichs. There also remains the possibility that Vorster will retire from public life which would be a sign that he is seriously ill. The nature of his sickness has not been disclosed but it is believed to be some kind of circulatory ailment.

The ruling National Party's 190-member caucus is to meet Stept. 29 in Cape Town to elect the new president and it would also elect a new prime minister then if necessary.

Vorster was elected prime minister in 1966. Since then he has become immensely popular among the country's 2.6 million Afrikaners - the whites of Dutch descent who dominate the government.

He was admitted to the hospital after the funeral of Deiderichs Aug. 26 for what described as a routine check. He stayed for several days of treatment for "fatigue and bronchitis" according to an official statement.

For the past week and a half he has been recuperating at his official residence in Cape Town, missing two Cabinet meetings, including one last week that involved a crucial discussion of the South West Africa (Namibia) situation.

Vorster's illness, coming only 10 months after his election victory last November, has sparked a battle among his potential successors.

Since the National Party is firmly in the grips of its hard-lines faction as far as racial policies go, Vorster's replacement is almost certain to be someone with hardline racial views.

The front runner, in the view of political observers, is Minister of Defence Piet Botha, 62.

But the party caucus could provide an occasion for the party's younger guard, who want a faster pace in removing racial discrimination, the granting of more rights to urban blacks and the holding of more meaningful consultations with black leaders.

So far this year the younger guard have not been able to make any significant imprint on the party's racial policies. But at a recent provincial party meeting, they rallied around Foreign Minister Pik Botha, 42. Some political observers say Pil Botha, who is regarded as a moderate, is being encouraged to think seriously about running for the prime ministership as a way to allow the moderates to display their strength in the party.