The 25-year-old actress and her boyfriend Boyd Holbrook are set to tie the knot after the 32-year-old star popped the question following two years of dating, according to Us Magazine.
A source said: "They've been by each other for a while, taking a lot of couple time."
The pair first met on the set of 'Very Good Girls' back in 2012 and have been inseparable ever since.
The loved-up duo took their relationship to the next level a few months back when they reportedly moved in together in Brooklyn, New York City.
The source explained: "They moved into a place in Brooklyn a few months ago."
Meanwhile, the Olsen family seem to be keen to head for the aisle as Elizabeth's older sister Mary-Kate, 27, also got engaged to her boyfriend Olivier Sarkozy, 44, just two weeks ago.
The fashionista is yet to confirm reports that the French banker proposed to her, but she has fuelled rumours recently by flaunting a diamond sparkler on her ring finger.
Mary-Kate and Olivier, who have been dating for two years, reside in New York, where they have a $6.25 million townhouse, but their union has caused some controversy due to their 17-year age gap.
Mary-Kate's twin sister Ashley is also dating an older man, with it recently confirmed she is seeing 47-year-old 'Moneyball' director Bennett Miller.