The 'Angels' singer - who has a house in Los Angeles' exclusive but quiet Mulholland Estate - was livid when the hotel heiress, famed for her wild partying, bought a home on his street.
A source said: "Paris has a new house right near Robbie's - and he's spitting mad about it. Robbie sped past her the other day in a chauffeur-driven car and completely ignored her. He hasn't any time for her and would rather they didn't have any contact."
The former Take That star - who celebrates his 34th birthday today
(13.02.08) - was dealt a further blow when it was revealed Paris is transforming her basement into a nightclub.
The source added to Britain's The Sun newspaper: "She is in the process of building a disco underneath her mansion so she can keep the parties going long after the clubs shut. If the late-nights start disturbing Robbie he will be absolutely furious."
Robbie moved to the US in 2002 to escape the pressures of fame in the UK. He has previously said he enjoys living in Los Angeles because he is virtually anonymous and can get on with his day-to-day life.