The Formula 1 driver - who rekindled his romance with Nicole over Christmas after splitting in July last year - is determined to persuade the 'Right There' singer to swap her London pad for his luxury home in Monaco.
A source told The Sun newspaper: ''Nicole is giving serious thought to moving in with Lewis.
''Both sets of families are behind them being back together and she and Lewis say it feels right.
''They know they can't keep splitting up and getting back together, so more commitment is the next step.''
Lewis - who started dating the brunette beauty in 2007 after meeting at the MTV Europe Music Awards in Berlin - promised the 'X Factor' UK judge that she can use his private jet to go to London whenever she wants, but she's still undecided about the relocation.
The source explained: ''After reuniting at Christmas, Lewis has decided he wants Nicole at his side for good.
''Nicole is always travelling all over the world with work, but rather than LA and London, Lewis wants their base to be in Monaco.
''They can go about there and no one pays them any attention, that's what he likes about the place.
''Nicole is mulling things over. They have been talking a lot about the future.''