"I believe that I have a responsibility to be with my family at this time," revealed the 38-year-old midfield schemer.
"I am very grateful for all the support we have received from the club and the fans and I hope to return to the club in the future.
Coventry City chairman Mike McGinnity has insisted that McAllister has the full support and sympathy of all at the club during a difficult time for the player-manager.
McGinnity added: "Myself and the whole board totally respect Gary's wishes to be with his family at this difficult time."