Speculation about a possible takeover comes amid a wave of dealmaking in the City. Low valuations have made even the biggest businesses possible targets, with UAE oil giant Adnoc recently exploring a bid for BP.
Burberry has been one of the worst performers on the FTSE 100 so far this year as demand for luxury goods slows, particularly in China.
Unusually for the industry, it operates as a single brand rather than as part of a larger group. Burberry competes against the likes of LVMH, which owns brands including Louis Vuitton, Stella McCartney and Dior, and is worth £400bn.
Consolidation is already underway in the US, where Tapestry – the owner of Coach handbags and Kate Spade – is currently pursuing a $8.5bn (£6.8bn) deal to buy Capri Holdings, the parent company of Jimmy Choo, Michael Kors, and Versace.
The Federal Trade Commission this week sued to block the deal on competition grounds.
Shares in Kering, which owns Gucci and Balenciaga, tumbled 6.8pc on Wednesday after warning it expects operating income to fall by up to 45pc in the first half of the year.
It follows an 11pc slump in first quarter sales, driven by weakness in China.
Not all luxury brands are struggling: Italy’s Prada, which also owns Miu Miu, reported an 18pc jump in first quarter retail sales, driven by a strong performance in Asia.
Burberry did not respond to requests for comment.