Whole Foods shares, which touched a more than 1-1/2 year high on Monday, were up 4.4 percent in afternoon trading.
Albertsons, the second largest operator of grocery stores in the United States, has had preliminary talks with bankers about making a bid, according to the report. (on.ft.com/2oEjJWa)
No formal bid has yet been made, the newspaper reported.
Whole Foods had a market cap of $11.38 billion as of Friday's close.
Sources told Reuters on Monday that Whole Foods hired investment bank Evercore Partners to defend itself against Jana Partners, but there were currently no plans for the company to explore a sale.
Albertsons, which is controlled by buyout group Cerberus Capital Management, said it did not comment on speculation, while Whole Foods declined to comment.
Earlier this month hedge fund Jana Partners disclosed a 8.3 percent stake in Whole Foods and said it intends to hold discussions with the company's board about exploring strategic options.
Reporting by Karina Dsouza in Bengaluru and Lauren Hirsch in New York; Editing by Shounak Dasgupta