Variety reports that Westwick is currently in final negotiations for the part, famously played by John Leguizamo in Baz Luhrmann's 1996 adaptation.
If cast, Westwick is likely to star opposite True Grit actress Hailee Steinfeld who is said to be the studio's first choice to portray Juliet.
Fluke director Carlo Carlei is scheduled to helm the project from a script by Gosford Park writer Julian Fellowes.
The Piano star Holly Hunter has also been cast in the key role of Juliet's nurse.
Steinfeld recently confirmed that the studio had yet to cast anyone in the lead role of Romeo.
Romeo and Juliet is due to begin filming later this year.