Australia’s Pat Cash begins his campaign against Mats Wilander on Wednesday, while McEnroe’s first match is on Thursday.
Cash and McEnroe could meet in the final again in a repeat of last year’s showpiece match after avoiding each other in the round-robin stages.
McEnroe has drawn Jeremy Bates and Andy Murray’s coach Ivan Lendl, while Cash and Wilander are grouped in with Henri Leconte.
The top player in each group from the field, which boasts 23 Grand Slam singles titles, will meet in Sunday’s final.
In the younger ATP Champions Tour event, Tim Henman and Goran Ivanisevic have been drawn together and will face each other on Saturday as part of the Winter Whites Gala, in aid of the charity Centrepoint.
Henman, the defending champion, will meet the man he beat in last year’s final, Thomas Enqvist, on Wednesday.