However back in March, the Shakespeare In Love actress made a rare declaration of love for the producer.
She shared a selfie on Instagram to wish him a happy birthday which marked the first and only time that she's posted about the American Horror Story producer.
It's a different tact for Gwyneth, who has previously enjoyed a string of very high-profile romances with the likes of Brad Pitt, Ben Affleck and her ex-husband Chris Martin, whom she shares two children with.
In a recent interview with Girlboss Radio, the Oscar-winning actress admitted she hadn't always had the best luck with romance in the past.
"I've f***ed up so many relationships," she said.
"I'm actually a pretty good friend, and a good sister and daughter and mother," she added.
"But I'm at my potentially most vulnerable and f***ed up in the romantic slice of the pie. It's taken me a lot of work to get to the place where I have a good romantic relationship."
She added: "Success to me is relationships that function really well. Where there is a beautiful feedback loop between people. I think without relationships of quality, you are not a successful person.
"So, if you don't have a good relationship with your partner, your children, your best friends, then it's really hard to claim success."
Rumours swirled over the summer that Gwyneth was preparing to wed current beau Brad, who also co-created Scream Queens.
She was snapped wearing a ring on her engagement finger while filming her role as Pepper Potts in Avengers: Infinity War, leading to speculation Brad had popped the question.
However, the talented actress cleared up the speculation by revealing on Instagram it was her character, Pepper, who was engaged to Tony Stark, rather than Gwyneth herself.
Gwyneth had quite the dating life while in the limelight as she famously dated her Seven co-star Brad Pitt as they were together from 1994 to 1997 and even were engaged at one point.
The Iron Man star's longest and most high-profile relationship was with Coldplay singer Chris Martin as they began dating in 2002.
They secretly married in December of 2003 in Southern California before welcoming two children together: daughter Apple Blythe in 2004 and son Moses Bruce in 2006.
In March 2014, she and the 40-year-old Fix You hitmaker infamously announced that they were 'consciously uncoupling'. Their divorce was finalised in July 2016.
After she split with Pitt back in 1997, Gwyneth moved on to a relationship with Ben Affleck as their on/off relationship lasted until 2000.
She then briefly dated Duets co-star Scott Speedman as they were spotted 'holding hands and nuzzling' at a Playboy mansion party in 1999.
Gwyneth kept the theme of dating co-stars going when she became involved with The Royal Tenenbaums co-star Luke Wilson for a year in 2001.
The talented actress has recently turned even more attention to her often controversial lifestyle brand Goop which she launched in 2008.
