The new rules mean vehicles and servicing for them can be sourced from companies outside manufacturers' franchises.
Derek Cook, chief executive of Motor Solutions, which runs an internet sales joint venture with wholesaler Makro, said: "The only reason retailers like Tesco have not clinched similar deals is that they are not as fast on their feet as Makro.
"We have been approached to talk to big retailers and wholesalers within and outside grocery."
A spokesman for Tesco said: "It's no secret we're seriously looking at selling cars. If we did, it would be on the internet."
Asda said it had no immediate plans but did not rule it out.
Morrisons already allows customers to buy cars from select outlets via terminals operated by internet vehicle merchant Lookers.
Meanwhile, Nisa runs its Miles More Value venture with a long-term lease company, offering a range of vehicles for rent through its retail members. Independent Nisa member Jempsons has already begun to display cars to rent for Â£99 per month outside its shops.
Cook said retailers could get special rates through such deals, which could drastically increase customer loyalty.