More than 100 stores are now online, and by the end of the year, that figure is expected to be 300, covering 90% of the population.
The Sunday Times says the plan is expected to be confirmed later this month when the UK's leading supermarket reveals its annual results.
Tesco was one of the first stores to embrace internet retailing, and now claims to be the world's biggest online grocer.
The new division - Tesco Direct - could eventually be floated. The paper says it could be valued at up to £4bn, more than a quarter of the parent company's market value.
Tesco launched its internet shopping operation in 1996, and has gradually been expanding.
More than 100 stores are now online, and by the end of the year, that figure is expected to be 300, covering 90% of the population.
Tesco Direct has 250,000 registered customers and annual sales of £125m.
Home shopping is still a small sector, but is expected to grow to a 10% share of the £120bn a year grocery market by 2005.
Tesco's rivals are also building up their internet businesses.
Waitrose delivers to customers in their workplace, and is aiming for 60,000 users by the end of the year.
Sainsbury's is now run by Sir Peter Davis, who established the Egg online banking brand while he was at Prudential.
Supermarkets are also leading the way in business-to-business internet applications.
Last week Tesco unveiled plans for a global retail exchange with 10 other big stores.
Reduced prices
It is hoped the greater purchasing power will lead to reduced prices for shoppers.
Sainsbury's is setting up a similar scheme with French supermarket chain Carrefour.
It is thought that separating the internet business from Tesco's core operations could allow it to expand internationally.
A full or partial float would also raise capital to set up special centres for the online service, rather than delivering goods from existing stores.
Like most supermarkets, Tesco has been under pressure to boost the company's share price, which has been hit by the current round of cut-throat pricing.