It also comes days after Foster, 49, filed for divorce from her husband, Ocean’s Eleven screenwriter Ted Griffin, on October 22 after 10 years of marriage.
Rumours about the relationship reportedly began during their stint as co-stars - and lovers - in the revival of the Broadway musical, The Music Man, which ran from December 2021 to January 2023.
The story follows con artist Harold Hill (Jackman) as he falls in love with the straight-laced librarian, Marian Paroo (Foster). The original play first opened on Broadway on December 19, 1957.
Insiders have since spoken to several media outlets about the stars, with sources telling Page Six the purported couple are keeping their rumoured romance under wraps - despite spending “all of their free time together”.
She had lead roles on the comedy-drama series’ Bunheads (2012-2013) and Younger (2015-2021), and appeared in three episodes of Flight of the Conchordsin 2007.
She has twice won the Tony Award for Best Actress in a Musical, with her Broadway credits including Thoroughly Modern Millie, Anything Goes, Grease, Little Women, Shrek the Musical, Violet, Sweeney Todd: The Demon Barber of Fleet Street, and The Music Man.
At the time of writing, Jackman and Foster haven’t publicly addressed rumours of their alleged relationship.
An insider previously told Page Six that Jackman and Foster were “100%” an item and “in love”, adding: “They ... want to spend the rest of their lives together”.
Another source said while the two “go out of their way to hide it”, their romance is “common knowledge” in certain circles.
Reports on the relationship have seen a 2022 interview with Jackman resurface, during which he gushed about Foster.
“Sutton Foster is just a dream,” he said at the time, adding: “I’ve been lucky enough to do films, and I’ve done some plays, but there’s nothing like doing a musical on Broadway”.
The two revealed they had decided to part ways in a joint statement issued to People on September 16, 2023.
“We have been blessed to share almost three decades together as husband and wife in a wonderful, loving marriage,” the former couple told the outlet.
“Our journey now is shifting and we have decided to separate to pursue our individual growth. Our family has been and always will be our highest priority. We undertake this next chapter with gratitude, love, and kindness.
“We greatly appreciate your understanding in respecting our privacy as our family navigates this transition in all of our lives.”
An insider claimed shortly after that the separation had been “a long time coming”, alleging there had been trouble in paradise for some time - even before Jackman returned to Broadway to perform in The Music Man.
“It happened a while ago. Friends and family knew about it,” the source said, adding: “Deb wasn’t at [The Music Man] rehearsals very much [and she] was even spotted snoozing during some of them”.