According to the Daily Mail, the production will run from 9 February to 27 April 2013 under the banner 'Traf Transformed'. It will be the first of four collaborations between Lloyd and designer Soutra Gilmour in the space, which is being backed by Ambassador Theatre Group (ATG).
McAvoy, 33, whose myriad film credits include The Last King of Scotland and X-Men, was last seen in the West End in Three Days of Rain in 2009 (which was also directed by Lloyd).
He told the Mail's Baz Bamigboye he wants to play the Thane before he gets "too old", adding: "I don’t think there’s any age he has to be, but in my mind he’s a captain of men and doing the fighting. He’s someone who has recently found out what it’s like to rip someone’s head off, stick it on a pike and stick it on a castle, and that sounds to me like a young man’s game."
Lloyd's recent stage directing credits include The Duchess of Malfi (Old Vic), She Stoops to Conquer (National), Inadmissible Evidence (Donmar) and The Faith Machine (Royal Court).
According to the Mail he is planning to set Macbeth in a "dystopian separatist Scotland" and is considering using an all-Scottish cast.