The report says Albertsons, which is operated by Cerberus Capital Management, is in "preliminary talks" to possibly take Sprouts private and add the organic grocery chain to join its rank of Albertsons and Safeway stores.
Citing people with knowledge of the matter, Bloomberg said discussions for the merger happened during recent weeks but the deal is still in its early stages and is not guaranteed.
Both Sprouts and Albertsons declined CNBC's request for comment.
Several Wall Street analysts released notes that said the deal would be a favorable move for Sprouts. Shares of the company are up 22 percent in the last week but are down 26 percent in the last 12 months.
Joe Agnese of CFRA Research kept a "hold" rating for Sprouts' stock after the report.
"We believe a potential deal makes strategic sense as increased scale would help [Sprouts Farmers Market] lower costs and price more aggressively in a low inflationary environment," Agnese said. But he added that he expects competition in the grocery space will "remain intense over the next few years."
Agnese has a price target of $24 on Sprouts shares. The stock closed at $21.82 on Monday.
Read more about the possible merger on Bloomberg's website.