The Ivorian is at odds with the club after allegedly being denied time with his brother, who died last week.
The 31-year-old's relationship with his club plumbed new depths Tuesday when the Ivory Coast star claimed that City denied him the opportunity to spend time with his brother Ibrahim, who passed away on June 19, prior to his death.
Relations between the player and the Premier League champion were already fraught after Toure accused the club of failing to properly acknowledge his birthday.
In an interview with France Football, Toure said: "I confess that I am still very sad. I'm suffering because I feel I have done nothing useful for him the last few weeks. At the end of the season, I wanted to stay for four or five days with my brother before I flew to prepare for the World Cup with Ivory Coast, except City did not want to give me a few days.
PHOTOS: USA vs. Portugal | U.S. fan reactions | Beautiful people in Brazil
"I went to celebrate the title championship in Abu Dhabi while my brother was in his sickbed. By fortune, Kolo was at his bedside. After that I blame myself for not insisting and for not leading them to respect me. However, club officials knew that I had been suffering for a few months seeing the health of my brother decline.
"This is the reason I had several injuries at the end of the season because my head had taken control of my body. These last four months have probably been the hardest in my life."
Toure and the Ivory Coast crashed out of the World Cup on Tuesday after a last-minute penalty from Greece's Giorgios Samaras condemned his side to group-stage elimination for the third World Cup tournament in a row.
City, which begins its preseason with a friendly against Dundee on July 13 before flying to the United States for the International Champions Cup, will now grant Toure extended leave before holding talks over his future.