The source also highlighted that "it would be very strange to replace a beloved cardinal before Christmas."
This latest development signals an imminent shift in leadership for one of the most prominent Catholic archdioceses in the world, and also just before Christmas.
Dolan has served as archbishop of New York since 2009, when Pope Benedict XVI appointed him after his tenure in Milwaukee.
Hicks, 58, could have emerged as a leading contender because of his Midwestern roots and reputation.
Born in Harvey, Illinois, and raised in South Holland, Hicks was appointed bishop of Joliet by Pope Francis in 2020.
His ties to Illinois and to the Chicago region, where Pope Leo also grew up, could be seen as strengthening his standing.
Speaking about the pontiff shortly after his election in 2024, Hicks told WGN-TV that the pope felt "relatable," noting, "He’s a normal guy from a normal neighborhood we grew up in."
On Monday, Rob Astorino, a Westchester County executive with ties to Dolan and the New York archdiocese, shared a post on X on the matter.
"Strong rumors that @Pontifex has accepted the resignation of @CardinalDolan and will appoint Bishop Ron Hicks of Joliet, Illinois," the post read.
If confirmed, Hicks would also take over leadership at a moment of difficulty for the Archdiocese of New York.
The church is confronting more than 1,300 clergy sexual-abuse claims, prompting an urgent need to raise approximately $300 million in settlement funds.
On Dec. 9, the archdiocese announced it would compensate victims, according to selling major real estate assets.
It also announced the $490 million sale of the land beneath the Lotte New York Palace Hotel, while another $100 million is expected from selling its former headquarters at 1011 First Avenue.
Fox News Digital has reached out to the Archdiocese of New York and the Diocese of Joliet for comment.