The couple - who have been staying in Canada with their 10-month-old son Archie since stepping away from royal life - are keen to have a base in Oxfordshire, which will be situated near private members retreat Soho Farmhouse.
Non-members can stay at the Cotswolds estate - which is where the duchess had her three-day hen party before marrying Prince Harry in 2018 - so the couple's guests will be able to stay nearby.
The property will be near a country home being built for David and Victoria Beckham and Harry and Meghan - who are said to be paying for the abode out of their own pockets - are planning a three-bedroom abode with its own drive.
A source told The Sun newspaper: "This house will be their bolthole when they are in the UK.
"It is costing around £3million and will be on the opposite side of the Farmhouse to the small house being built for the Beckhams."
The couple are good friends with the Beckham and David recently praised Harry for focusing on being a dad.
He said: "I haven't spoken to Harry about him moving. We speak as friends and that's the most important thing for me. I think he's enjoying being a young father for the first time and that's what we always spoke about. When you are a parent, it changes everything for you. He always needs to be happy."
David and his wife Victoria Beckham attended Harry and Meghan's wedding in May 2018, and the sports star has loved seeing his pal become a family man.
He added: "We love him and he's an amazing person - and that's the most important thing - but I'm proud to see him growing up as an individual and being that person that every father wants to be. Every father wants to be loving to their children and that's what I see with him."