The Brazilian owner of the Body Shop is set to buy Avon Products in a deal that is expected to value the US cosmetics company at more than $2bn (£1.58bn).

Natura Cosméticos said it was in “advanced discussions” with Avon, following a report in the Financial Times. After the deal, it is expected that Natura would control more than three-quarters of the combined group. The remaining shares would be owned by Avon shareholders.

Avon, founded in 1886 and known for its doorstep-selling model, has its headquarters in London but is listed in New York with a market value of about $1.4bn. In January, the company announced plans to cut about 2,300 jobs – 10% of its global workforce – as it sought to find cost savings of almost $100m.

The company has struggled to keep pace with changing consumer tastes and habits, and competition from rivals that have capitalised on the growth in online beauty sales.

The rise of social media has fuelled rapid change in the beauty market, helping to launch new brands backed by online influencers, such as Rihanna’s Fenty Beauty and Kylie Jenner’s lip kits, which are challenging established names around the world.

Both boards have agreed to the all-share deal after months of talks. Avon would give São Paulo-based Natura Cosméticos a bigger share of the market in Brazil and other Latin American countries, as well as in Europe and Asia.

However, the tie-up does not include Avon’s north American business, which was spun off three years ago as part of an effort to reduce debts.

The planned deal comes after a string of acquisitions by Natura, which have extended its international reach.

The group bought the Sussex-based Body Shop from L’Oréal in a €1bn (£877m) deal in 2017. It also owns the high-end skin and haircare brand Aesop and is already Brazil’s largest cosmetics company with revenues of $3.4bn in 2018, up 36%. It has a market value of about $6.2bn.

The company was founded in 1969 in São Paulo by Antônio Luiz Seabra, who remains its biggest shareholder. In 2014, Natura became the first publicly traded company to be certified as a B Corp, meeting certain standards of social and environmental performance and transparency.

Natura said in a statement on Wednesday: “The company confirms that it is in advanced discussions with Avon concerning a potential acquisition of Avon, to acquire Avon by means of an all-share merger, that would result in the combination of the businesses, operations and shareholding bases of Natura and Avon.

“The parties are currently negotiating final contractual terms of the transaction. There can be no guarantee that a definitive transaction will be announced or the other terms of any such agreement.”