Burke along with Keith Hammill, the chairman of fashion retailer Moss Bros, has made an offer believed to be in the region of £850m.
Their bid has the backing of Permira, the private equity group which has £7bn under management.
It might be hard for WH Smith to refuse the offer given that WH Smith’s collapsing share price has seen the company now valued at around £630m.
Hammill and Burke are returning to familiar territory. Hammill was WH Smith’s finance director in the 1990s, while Burke was managing director of its then subsidiary, Virgin Our Price.
According to reports, Hammill and Burke held a meeting with WH Smith’s chief executive Kate Swann last week.
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