A month ago Wal-Mart Stores (NYSE: WMT) said it was making a non-binding offer for South Africa’s Massmart Holdings Ltd. and that it would enter exclusive discussions with Massmart that could last for an indefinite period.

The deal Wal-Mart proposed in September was a total buyout of the South African wholesaler for about $4.6 billion. Now, The Wall Street Journal reports,  Wal-Mart is considering taking a majority stake only. Wal-Mart has already done such a deal with Massmart’s Mexican subsidiary, in which the retailing giant owns 68%.

Apparently Wal-Mart has run into resistance from South African labor unions, which note the company’s long-held status as a union basher. Imagine that.

When investors got wind of the possible change in Wal-Mart’s planned buyout, Massmart shares fell 3% on fears that Wal-Mart was planning to pull out. Wal-Mart also noted that Massmart’s shareholders and others in South Africa have asked the company to consider just a partial buyout.

Wal-Mart is also considering whether or not to retain Massmart’s listing on the Johannesburg Stock Exchange. The JSE would undoubtedly prefer that course. The government of South Africa would also like to see Massmart retain a listing on the JSE.

Wal-Mart made the offer for Massmart to gain a foothold in Africa. Massmart’s strength is its general merchandise wholesale business, but it also has a food business and that is what Wal-Mart wanted most. Why pay $4.6 billion for that when you can get control of the company with half that amount plus a dollar? Once Wal-Mart has control it can do what it wants.

The only reason to acquire 100% of Massmart is to add to Wal-Mart’s top line. For Massmart’s fiscal year ended in June 2010, the company’s revenue totaled about $6.8 billion, which would add less than 2% to Wal-Mart’s annual revenue.

Taking a controlling stake in Massmart would make everybody happy, so that’s what Wal-Mart is likely to end up doing.