The striker handed in a transfer request in December but then committed his future to the club, who won their first major trophy in 35 years in Saturday's FA Cup Final.
"I don't have problems with anyone at the club, things are fine (with coach Roberto) Mancini and everyone, but it's a decision I need to discuss with my family whether I stay or not," he was quoted as saying by several British newspapers on Monday.
"My family, my kids are a long distance away from Manchester and if there is an option to go then it will be something to do with my family and children. It would be a personal decision rather than a professional one."
City have plenty of forward options and could buy another top striker thanks to their Abu Dhabi owners but Tevez's importance to the side was underlined by Mancini rushing him back from injury to start on Saturday.
The former Manchester United striker would be welcomed back by clubs in Argentina but whether they could pay the price expected by City is unlikely.
A move to another European team would leave City fans scratching their heads given the travel time to Argentina would be little different.
"It is not only distance that matters," Tevez added cryptically.
