Jude Law and Sienna Miller are looking to buy a new home together in the London suburb of Highgate.
The couple - who are reported to be engaged for the second time - are looking to purchase a new home in London, and are tempted by a £4 million pad in Highgate, north London.
A source said: "They've looked at a few properties in the north London area.
"They've taken a real fancy to a £4 million six-bedroom period property near their favourite pub in Highgate. They have decided to snub Sienna's beloved Notting Hill and Primrose Hill.
"Buying in Highgate means they can still walk to Hampstead in minutes and Jude will be just around the corner from ex-wife Sadie Frost and their children."
Jude - who has three children, Rafferty, 13, Iris, nine, and Rudy, seven, with Sadie and another daughter, seven-month-old Sophia, with model Samantha Burke - separated from Sienna for the first time in 2005 following allegations of an affair with nanny Daisy Wright
But they rekindled their romance last year and were seen on a Caribbean holiday together over the 2009 festive period.
Yesterday (12.04.10), it was reported the pair had got engaged again after the 'Factory Girl' actress was seen wearing the vintage diamond ring Jude had given her during their first engagement - but on her right hand.
A source said: "They do not want to make the engagement official which is why Sienna is wearing the ring on the wrong hand.
"They are keeping it secret, but are very happy and really hope it's going to work out.
"Jude has been to visit Sienna's parents and her sister Savannah and has worked hard to redeem himself."