"Pipavav is talking to a large international player. It would take about one or two weeks for the deal," the source said.
India's largest shipyard by market capitalisation hopes to sell the shares at a 20 percent premium to its current market price, the source, who declined to be identified ahead of a public announcement, told Reuters.
At the current market price, this would come to more than 100 rupees a share.
Earlier on Tuesday, Pipavav shares rose nearly 10 percent after a television channel reported the firm was in talks to sell a stake. At 2:30 p.m. the shares were up 8.64 percent at 88.65 rupees in the Mumbai market.
Pipavav Shipyard's promoters currently hold about 45 percent in the firm, data from the stock exchange showed.