Such a change could amount to almost £200m in payments a year, The Telegraph reports. It would apply if a landline or broadband internet service goes down and is not fixed quickly enough, or by the day that is promised, and if an engineer does not arrive for a scheduled appointment.
Earlier this month BT agreed to make its broadband infrastructure division Openreach a separate company, following pressure from Ofcom.
Ofcom's consumer group director Lindsey Fussell said: "When a customer's landline or broadband goes wrong, that is frustrating enough without having to fight tooth and nail to get fair compensation from the provider.
"So we're proposing new rules to force providers to pay money back to customers automatically, whenever repairs or installations don't happen on time, or when people wait in for an engineer who doesn't turn up. This would mean customers are properly compensated, while providers will want to work harder to improve their service."