The Telegraph reports the yacht, a successor to the Royal Yacht Britannia which was decommissioned in 1997, could cost as much as £200 million.
It is expected that Prime Minister Boris Johnson will announce the news “within weeks”, with a spokesperson from Downing Street saying: “The prime minister has an exciting vision for shipbuilding in this country and is committed to making the UK a shipbuilding superpower.
"We are always looking for new ways to promote global Britain around the world, driving investment back to the UK and delivering value for money for the British people."
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The Duke of Edinburgh was Lord High Admiral for the decade before his death on April 9, 2021, and during the Second World War he served in the Royal Navy.
MPs are calling for the vessel to be built in the UK, with conservative MP Craig McKinlay saying: “A new national flagship proudly bearing the name of Prince Philip can be no better memorial to this much-loved and respected man.
"My latest joint letter signed by fellow MPs and peers may have helped get this project over the line. I am overjoyed."
Chairman of the Northern Research Group of MPs, Jake Berry, has called for the new vessel to be built on Merseyside by Cammell Laird.
The yacht would be expected to sail all around the world and be used to promote British trade and interests overseas.
Since being decommissioned, the Royal Yacht Britannia has been berthed in Leith, Edinburgh and used as a tourist attraction, although it was closed for the majority of 2020 as a result of the coronavirus pandemic.
Prince Phillip died aged 99 on April 9, 2021, at Windsor Castle after spending a month in hospital earlier this year.
He initially received care for an infection but then underwent heart surgery for a pre-existing condition.
The duke was the longest-serving consort in British history.
He and the Queen were married for more than 70 years and he dedicated decades of his life to royal duty, serving the nation at the monarch’s side.
He officially retired from public engagements in the summer of 2017.
He was just two months away from his 100th birthday when he passed away and his death has been described as the nation “losing its grandfather”.