The talks have stalled but could be revived, the source said on Tuesday.
A potential deal between ConAgra and Post Holdings could value Lamb Weston at around $6 billion, said another source with knowledge of the matter.
ConAgra, the maker of Chef Boyardee pasta and Slim Jim beef jerky, said in November last year that it would spin off its Lamb Weston business into a separate, publicly listed company.
The Wall Street Journal first reported the talks earlier on Tuesday. (on.wsj.com/28Lrq60)
The two companies were discussing a Reverse Morris Trust structure for the deal, the first person said. A Reverse Morris Trust is a tax-free deal in which one company merges with a spun-off unit.
ConAgra spokesman Mike Cummins said the company did not comment on rumors or speculation.
Post Holdings was not immediately available for comment.
Reporting by Subrat Patnaik in Bengaluru and Lauren Hirsch in New York; Editing by Kirti Pandey