Walmart has begun discussing a possible acquisition of health insurer Humana, The Wall Street Journal first reported Thursday citing people familiar with the matter. Reuters also reported the companies are discussing a partnership, but that a full acquisition is also possible.

Shares of Humana soared as much as 13 percent in after-hours trade on Thursday. Walmart shares edged slightly lower in extended trade.

The newspaper said that details of the potential deal were not immediately clear and that it's possible one may not materialize.

Walmart said in a statement to CNBC that it doesn't comment on rumors and speculation. Humana did not immediately respond to CNBC's request for comment.