She made the statement in her interview to Sky Sports.
Williams, who has won 38 major titles in her career, said that she would not encourage her children but would also not stop them if they decide to take up the sport.
Serena added, “I wouldn’t want the stigma of mummy Serena, I think that would be a lot of pressure and I would like for them to do their own thing and have their own name and be the best at whatever they wanted to do.”
The former champion stated that she was facing health issues since Wimbledon this year.
She faced a third round exit in the 2016 Rio Olympics and was knocked out of the US Open by Karolina Piskova in the semi final of the grand slam this year.
German Angelique Kerber took away her top spot in the ranking, which she held for 186 weeks straight.