The couple, who broke up in 2005, have found themselves back in the same neighbourhood – Sienna is starring on Broadway in After Miss Julie, while the dad-of-four is receiving rave reviews for Hamlet - and are said to have become close again.
At lunchtime on Wednesday, the 27-year-old blonde was seen leaving Jude's home minutes after he exited.
Reports also suggest they celebrated Thanksgiving with a late night Italian meal in the city, and that Sienna has been cooking meals for them both after their shows.
One friend has said Jude has told ex-wife Sadie Frost about his reconnection with Sienna, and that his best friend Jonny Lee Miller – starring alongside the Factory Girl star in her play – originally brought them back together as friends.
"They are taking things incredibly slowly, but they are getting back together again," the source added.
But Sienna's sister, fashion designer Savannah, has dismissed the suggestion of a reunion.
"I think it would be a completely ridiculous assumption considering the way that man has conducted himself recently. That's all I'm saying," she said.
Since the end of their relationship four years ago, Sienna has been romantically linked to married father-of-four Balthazar Getty, who has since gone back to his wife, Welsh actor Rhys Ifans and DJ George Barker.
Jude, meanwhile, became a father for the fourth time in September following a brief affair with Samantha Burke. His baby daughter Sophia and her mother were featured exclusively in HELLO!.