The 35-year-old is reportedly planning a 'boys' day' out for him and Katy's father, Keith Hudson.
A source told British newspaper The Sun: 'When Katy first introduced her mum and dad to Russell, it was no secret they weren't too keen on him. They'd done their research and did practically everything they could to wean Katy away from him.
'But over the past few months things have taken a dramatic change and Keith has told pals that Russell is 'the perfect son-in-law.''
The source added: 'He even calls and texts Russell and they have arranged a lads-only day out together over Christmas.'
The 26-year-old Firework singer and Brand are spending Christmas stateside in Los Angeles.