Teigen asked Ms Ocasio-Cortez, who represents New York’s 14th congressional district, if she wanted to join her and Modern Family star Jess Tyler Ferguson to watch the 61st awards ceremony.
Teigen tweeted: “Hello my hero, do you wanna come over and watch the Grammys with us? There will be pizza.”
After this, she asked Ms Tyler Ferguson to tell Ms Ocasio-Cortez “we are normal”.
The Democrat, who is the youngest ever US congresswoman, said: “Yes! We can live-tweet me burning something in the kitchen.”
“Perfect! We have extremely different strengths except I still sometimes burn things,” Teigen, one of US president Donald Trump’s most outspoken and cutting celebrity critics, replied.
The nascent friendship prompted great excitement on social media – with some asking if they could join in on the revelry.
“Name a better duo, I’ll wait,” tweeted Jules Suzdaltsev.
“This type of wholesome interaction is the reason why I still have twitter wow,” one person wrote.
“This is the crossover I didn’t know I needed but can’t wait to witness,” added another.
Ms Ocasio-Cortez worked as a bartender before thrashing Democrat stalwart Joe Crowley – the 10-term representative and then-fourth-ranking Democrat in the House – last year.
The self-avowed socialist, from the South Bronx, has worked as a waitress, children’s book publisher, community activist, a member of the Democratic Socialists of America and volunteered for Bernie Sanders during his 2016 presidential campaign.
She supports abolishing the Immigration and Customs Enforcement agency and the creation of a universal healthcare system. Already this year, she has asserted that Mr Trump is “no question” a racist, and beaten back a manufactured controversy over a video of her dancing while in university.
Teigen is similarly critical of Mr Trump and started trolling the billionaire far before he announced his presidential bid. In 2017 she told USA Today: “I’ve actually been a big Donald Trump hater for a long time. If you go back, I’ve been trolling him for about five to seven years now.
“I’ve been doing this forever and I take pride in that ... I can’t believe somebody could actually do this all day, every day, and still be president. If I mysteriously go missing in the next four years then that’s what happened.”
The Grammys will be held on 10 February in Los Angeles. It will start at 5pm PST, which is 1am on Monday in the UK, and is being broadcast live on CBS from the Staples Center in the city.
They are set to be hosted by Alicia Keys. Cardi B, Shawn Mendes, Janelle Monae, Red Hot Chili Peppers with Post Malone, and Miley Cyrus are scheduled to perform.