The first movie, which starred Brie Larson as the iconic comic book character, was directed by duo Anna Boden and Ryan Fleck and made $1.13 billion at the global box office.
According to Deadline, Marvel chiefs have been taking meetings with prospective directors for the sequel over the past few months and have decided on DaCosta to take over from the pair, directing from a script by WandaVision story editor Megan McDonnell.
If her hiring is confirmed, it means the 30-year-old will be helming the biggest budget movie ever made by a black female filmmaker as its cost will likely dwarf the $115 million (£87.4 million) budget of Ava DuVernay's "A Wrinkle in Time".
The reported move would continue Marvel's push to increase the diversity of its stable of directors, with Asian-American Chloe Zhao taking charge of "The Eternals" franchise.
DaCosta is a rising star in Hollywood, following her critically acclaimed indie movie "Little Woods", with Jordan Peele, picking her to direct his Candyman reboot - a film whose trailer has made waves on social media even though its release has been delayed due to the Covid-19 pandemic.