The pair star together in historical drama 12 Years a Slave, and Lupita won the Best Supporting Actress trophy at the Academy Awards last Sunday for her work in the film.
Michael was physically demonstrative with Lupita throughout the ceremony, and sources claim the co-stars were once lovers.
“They have an incredible connection after the whirlwind of filming 12 Years A Slave and then promoting it together,” a source told British newspaper The Sun.
“In September during the Toronto Film Festival they had a brief romance.”
Apparently Michael is so enamoured with Lupita he recently called it quits with Romanian supermodel Madalina Ghenea.
The outlet also reports he decided to bring his mother to the Academy Awards, so that Lupita is clear she is the only woman he wants in his life romantically.
“Now Michael is intent on showing how he wants to get serious again and made a point of bringing his mum Adele to the Oscars rather than a date,” the insider explained.
“Lupita’s the most in-demand woman in the world at the moment so it will be hard to make it work but their chemistry is undeniable.”
Lupita has been linked to other Hollywood hunks of late, including fellow Oscar-winner Jared Leto.
But both stars have denied they are dating each other, despite reports to the contrary.
Michael has romanced a castmate before, as he was with X-Men: First Class co-star Zoe Kravitz from 2010 to 2011.
He has spoken previously about how his hectic work schedule impacts relationships.
“I'm kind of selfish with the hours that I put into the work,” he revealed in the November 2013 issue of GQ.
"I think the longest relationship that I’ve been in was two years. I started doing this when I was 17, so I guess in my dating, adult life, that kind of covers it."