Amakhosi have also announced the promotion of 19-year-old Njabulo Blom from their reserve team.
Phakaaathi reported that Parker had agreed to a one-year contract extension with the club on Monday.
Chiefs have since confirmed that Parker will stay at Naturena for one more season with an option to renew for one more year.
“Bernard Parker has signed a 1 year contract extension with a 1 year option,” read a tweet from Chiefs.
“We would like to confirm the promotion of 19-year-old Njabulo Blom from our Reserve Team. He has signed a 4 year contract,” read another Chiefs tweet.