The first move could save the company between £100m and £650m and the second between £150m and £650m, according to the regulator.
It comes after Rishi Sunak, who would have to approve any changes, appeared to rule out Royal Mail being allowed to scrap Saturday deliveries.
But Ofcom chief executive Dame Melanie Dawes said that changes to the postal system could be required as the number of letters being sent each year has halved since 2011, while people are getting many more parcels than they used to.
Currently, Royal Mail has an obligation to deliver letters six days a week to all 32 million addresses in the UK for the price of a stamp, no matter where the letters are going.
Royal Mail, which recorded a £419m loss in its previous financial year, said the current service requirement is “simply not sustainable”.
Dame Melanie said: “Postal workers are part of the fabric of our society and are critical to communities up and down the country. But we’re sending half as many letters as we did in 2011, and receiving many more parcels.
“The universal service hasn’t changed since then, it’s getting out of date and will become unsustainable if we don’t take action.
“So we’ve set out options for reform so there can be a national discussion about the future of universal post. In the meantime, we’re making sure prices will remain affordable by capping the price of second-class stamps.”
Mr Sunak’s official spokesperson said the PM’s “strong view is that Saturday deliveries provide flexibility” and “would not countenance” seeing Saturday deliveries scrapped.
The postal minister Kevin Hollinrake reiterated on Wednesday that government remained committed to a six-day service from Royal Mail – calling a Saturday delivery “sacrosanct”.
Neither the minister nor No 10, have said whether they would be prepared to legislate to keep a Saturday delivery.
Mr Hollinrake told Times Radio: “The prime minister has been very clear on this, six-day delivery is really important for many people in this country, many of our citizens – but also for many of our businesses.”
The Tory minister also said that nationalising Royal Mail would not be a “good option”. He said the “one advantage” of it remaining in private hands is “the amount of investments going in”.
The Liberal Democrats’ Treasury spokesperson Sarah Olney said the idea of a three-day delivery “feels like a slap in the face”, adding: “Regular deliveries are what the country has come to expect.”
The Federation of Small Businesses (FSB) warned that cutting the six-day delivery service could “cause real disruption to our economy”.
And the Communication Workers Union (CWU) said a three-day delivery service would “destroy” Royal Mail.
CWU general secretary Dave Ward said: “We are not resistant to change, but we will not sign up to a three-day universal service obligation, which would destroy Royal Mail as we know and would impact thousands of jobs.”
The Post Office, which was spun off when Royal Mail when the latter was privatised in 2012, said many people and businesses “depend on a reliable letter service”.
Under fire over the Horizon IT scandal, a Post Office spokesperson said there must be a “national debate” around how consumers need a parcel and letter delivery service to work for them in the 2020s.