The couple have been eyeing a £6m ($9.5m), eight-bedroom property in Brentwood, and are said to be making the move in order to be closer to their friends and Paltrow's mother Blythe Danner.
"They've wanted to move to LA for a while now," a source told The Mirror. "Gwyneth spends lots of time between the UK and US and is exhausted with travelling. She spends a lot of time away from her mum, so she wants to be closer to her as she gets older.
"Chris was understanding and is willing to try as he's always loved the city. His band won't be working on an album for a year, so he has space to kick back."
Paltrow was recently reported to be backing a British version of the charity telethon Stand Up to Cancer for Channel 4, which is due to air in mid-October.
Martin, meanwhile, continues to tour with Coldplay and will perform with the group at the Paralympics closing ceremony next month.
Watch the music video for 'Paradise' by Coldplay below: