That decision came after an intense debate at Monday's city council meeting.
However, most of the members of council who spoke on the proposal, including Mayor Michael Fougere, said they were against heritage designation.
The foundation of the school is crumbling, there's asbestos and an engineering report says it's not structurally sound.
One councillor, Shawn Fraser, called for a heritage inspection on the building, but he couldn't get a seconder and his motion died.
After more debate, council voted against heritage status.
It was a disappointment to Bill Brennan, the president of Heritage Regina, who said Connaught was the oldest school still being used for its original purpose.
It's an important part of the culture and history of the Cathedral neighbourhood, he said.
The Regina public school board chair Katherine Gagne said she hopes Cathedral will have a new school on the same site by 2017.
Connaught is closing at the end of the current school year. Students and staff will move to Wascana School at at 4210 4th Ave. until a new one is built.