The Radiohead lead guitarist and keyboardist-turned-composer is up for Best Original Score at the 90th annual awards alongside Hans Zimmer (Dunkirk), Alexandre Desplat (The Shape of Water), John Williams (Star Wars: The Last Jedi) and Carter Burwell (Three Billboards Outside Ebbing, Missouri).
His score for the historical drama – which stars Daniel Day-Lewis and Lesley Manville – also received a nomination for Best Original Score at last year’s Golden Globe Awards as well as a BAFTA nomination this year.
Phantom Thread is the fourth film Greenwood has scored for director Paul Thomas Anderson.
Since turning his hand to film scoring in 2003, Greenwood has composed for films including We Need to Talk About Kevin, The Master and You Were Never Really Here.
This year's Oscars take place on 4 March at the Dolby Theatre in Hollywood, California.