The Spice Girl has just moved to Los Angeles with her soccer star husband David but isn't interested in the hotel heiress' party invitation.
Paris is reported to have said about Victoria: "We could be soulmates." However, Victoria apparently told a friend: "Over my dead body!" Sources claim Victoria – who counts Tom Cruise and his wife Katie Holmes and Jennifer Lopez among her good friends – believes being associated with Paris could have negative consequences for her.
Victoria – also known as Posh Spice - is keen to establish herself as a major Hollywood player and doesn't want Paris, who recently served time in jail, to interfere with that.
Meanwhile, Victoria's American TV debut has been slated by critics.
The reality show, 'Victoria Beckham: Coming To America', followed the singer as she prepared to move to Los Angeles after David signed with soccer team Los Angeles Galaxy.
It was aired in the US at the weekend but it failed to win over many reviewers.
Linda Stasi of the New York Post gave it "no stars" and labelled it "an orgy of self-indulgence", while The New York Times' Alessandra Stanley described her as a "rich idiotic It girl".