The global drugstore chain Walgreens Boots Alliance has reportedly received a buyout offer from the private equity group KKR – if successful, the deal would be the biggest private equity transaction on record.

Shares in Walgreens Boots Alliance rose 6% on Monday after Bloomberg reported news of the deal. Its shares had fallen nearly 20% between January and the end of October, before news of a potential buyout emerged.

Walgreens Boots Alliance, which owns Walgreens and Duane Reade in the US, Boots in the UK and a number of pharmaceutical manufacturing and distribution companies, operates in 25 countries and has more than 415,000 employees.

It has struggled in recent years and is currently closing stores and cutting jobs in an attempt to save $1.8bn a year in costs by 2022. The company is facing stiff competition from online sales as consumers increasingly buy household staples online, a trend that is rapidly expanding to pharmaceuticals too. Slowing revenue from prescription drugs have also hurt the company.

Last year Amazon bought the online pharmacy PillPack in a deal widely seen as an indication of Amazon’s intent to push further into the healthcare industry.

Chairman Stefano Pessina, who owns about 16% of the company, built Walgreens Boots Alliance through a series of takeovers. KKR helped Pessina buy Boots Alliance in 2014 in what was Britain’s largest ever management buyout.

Despite the company’s size it has struggled. The company is currently reviewing its store portfolio and in May Boots said it could close up to 200 stores over the next two years, the latest in a series of high street names to announce drastic closures. In a call with analysts earlier this year the company also blamed Brexit for “challenging” conditions.

In the US Walgreens’ largest rival, CVS Health, has repositioned itself as a healthcare giant, merging with the insurer Aetna. Walgreens, in contrast, attempted to expand its portfolio with an unsuccessful takeover of rival Rite Aid and has since announced a deal to expand with other retailers, including the grocery chain Kroger.

With a market value of $56bn and $16.8bn in debt, the price to take the company private would top the largest leveraged buyout in history: the 2007 sale of utility TXU to KKR and private equity investment firm TPG, which was worth about $45bn, according to data compiled by Bloomberg.

Some finance chiefs are skeptical about a deal. “It might be possible. It’s a huge stretch doing things over $50bn,” Stephen Schwarzman, head of Blackstone, one of the world’s biggest buyout firms, told a Reuters Newsmaker conference last week.