Watch: Eternals cast discuss keeping secrets
The Mexican actor plays Ajak in the new Marvel movie (in IMAX and cinemas from 5 November), who is depicted as the leader of the group of super-beings and the only one capable of communicating with their Celestial mentor Arishem.
She told Yahoo she is 'not good' at keeping secrets and struggled to keep her involvement in the MCU under her hat.
Read more: On set secrets from the Eternals shoot
"You can keep a bad secret easily, but you want to brag about something like this," she said.
"We've been waiting for this moment for a long time. I have a lot of friends who are superfans of Marvel, so it was tough."
But Hayek said there was one scenario in which her mask slipped, while she was working with Samuel L. Jackson aka Nick Fury and Ryan Reynolds aka Deadpool — on The Hitman's Wife's Bodyguard.
"They were talking about the Marvel universe. I wanted to tell them 'I'm part of this conversation by the way'," said Hayek.
She added: "I couldn't say anything, but I was paying attention to everything they were saying and I was just dying to tell them. I was almost like a little dog when they were talking about it.
"[Jackson] said: 'So, how much are they paying you? Which one are you gonna be?'
"I was like 'what are you talking about?' and he was like 'you know what I'm talking about, that secret?'. I said 'how do you know?' and he said 'I can smell it on you'."
Hayek may have struggled with keeping secrets, but many of the other Eternals cast members were far more capable of maintaining absolute silence.
Kit Harington, who portrays museum worker Dane Whitman — boyfriend of Gemma Chan's superhero Sersi — said his time on Game of Thrones has made him a great secret keeper.
He said: "I think it was the world's best schooling in avoiding spoilers or actually giving you lovely people anything interesting to write. I think I had a good education in not spoiling things."
Chan herself said that the cast had to sign huge contracts and NDAs, joking that "there's always a sniper trained on you at all times".
Richard Madden, who plays the incredibly powerful warrior Ikaris, said the closeness of the cast made it easier to keep things under wraps.
He said: "A good thing is that we're in the film together and we've been friends for a long time.
"We have someone to share all the secrets with and get excited about things and talk about it, so that we don't do it to other people."
Hayek, meanwhile, said she had some trepidation about taking on the role of Ajak, who has always been portrayed as male in the comic books.
She added: "My super-power is healing and I think leaders should be healers at heart. They should want to go into power to heal a society, to heal the people, to heal the differences between them. We don't have that in real life, so I think it was lovely to have somebody that was very sensitive — not just very tough."
Eternals is in IMAX and cinemas in the UK from 5 November.
Watch: Trailer for Eternals