Jackman, 56, and his former Music Man costar, 49, went public with their romance on January 6 with a hand-in-hand dinner date in L.A. after months of sneaking around on the sly, insiders added.
As previously reported, sources said Jackman was smitten with the married Broadway beauty during their stage stint - and rumors of romance intensified as he and Furness separated in September 2023 and Sutton filed for divorce last October from screenwriter Ted Griffin.
Sources added spurned Furness didn't look thrilled to be bundled up in the Big Apple - the city she and her soon-to-be ex-husband had long called home.
But an insider said: "She and Hugh need to sort through some unresolved issues regarding their assets and expenses and possible settlements."