The British fashion chain received an approach from Coach, but binned a deal that valued the company at over $20bn, according to the Financial Times.
The talks between the two companies were active over the summer, with a view to Coach making a cash-and-stock takeover of Burberry. It is thought the deal would have gone ahead if Coach had made a move earlier in the year.
Burberry's shares hit their lowest ever level in June at £14.11, but have since climbed to £14.40.
Both Coach and Burberry have refused to comment on the reports.
Rumours about the deal have been floating around for some time. In October, financial blog Betaville said Coach had engaged investment advisory firm Evercore to work on a potential tie-up.
The British fashion house has said that it could be in for a £125m windfall due to the slump in the value of the pound since the Brexit vote. But, its declining revenues and profits have been weighing on its share price.
Coach is known for its leather goods and handbags, while Burberry is more famous for its outwear - but the two are similar in terms of how they position their brands: