Shop Direct has sent a legal letter to Alworths over the use of its name as the group argues it is too similar to Woolworths.
If it does not alter its plans, Shop Direct will take further legal action, according to the Financial Times.
The move comes just days before Alworths – led by former Woolworths director Andy Latham – is due to open its first high street shop.
The challenge is partly driven by the fact Shop Direct has not ruled out bringing Woolworths back to the high street through a licensing agreement.
Shop Direct chief executive Mark Newton-Jones said: “We think there is an opportunity [for] a chain of stores in towns across the UK. That is even more of a reason we would defend our position.”
Alworths is due to open its first shop next week in Didcot, and plans to have a further four shops open by Christmas.
Latham said: “We can confirm that we have received correspondence from lawyers of Shop Direct. This is a legal matter that we are considering with our lawyers.”
Newton-Jones said Shop Direct had no issues with Wellworths, the shop opened by a former Woolworths manager in Dorset.