Related Video: Hugh Jackman and Russell Crowe sing-off in New York pub
According to a source, the pair were spotted fireside at Greenwich Hotel at 3AM on Sunday morning in New York. "They seemed to be in an intense flirtatious conversation," the source said, adding, "They looked really into each other."
The pair were spotted again at the hotel later in the day. "Katie was still at the hotel Sunday afternoon," the source said. "She was seen with Crowe at the same fireplace at about 2 p.m."
Russell is currently filming "A Winter's Tale" in New York alongside Colin Farrell.
Katie was also spotted at Joe's Pub with Russell in New York on Sunday night, who was there to support his "Les Miserables" co-star Hugh Jackman. The pair indulged in a battle of the voices, reprising their "Confrontation" song battle from the musical (you can watch them sing at the top of this page).
When reached for comment, Russell's rep dismissed the dating claims, saying he and Katie were "just friends".
Katie Lee divorced Billy Joel in 2009 after five years of marriage, walking away with a substantial settlement.
Russell separated from wife Danielle Spencer in October this year after nine years of marriage. The pair have two sons.
Related Video: Watch the trailer for "Les Mis"