The couple have made appearances together at a series of high society New York City events in recent weeks, sparking rumours that they are in a romantic relationship.
A source close to Cattrall told Page Six that the actress and Ross have in fact begun a low-key fling, saying: "[Ross] has no agenda with Kim, he's not the type to date a celebrity; he likes her."
Cattrall's spokesperson denied those claims by insisting that the pair are "just friends".
Ross - whose photographs have been displayed in the Whitney and the Guggenheim - is currently in the midst of a divorce with wife Betsy Finkle Ross.
Cattrall has been single since splitting from third husband Mark Levinson in 2004.
The actress admitted last summer that she would love to marry for a fourth time provided that she met the right person.
Cattrall's Sex and the City co-star Kristin Davis has recently been linked to Oscar-winning screenwriter Aaron Sorkin.
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