Sylviane Finck Lozada was reported missing from her Baton Rouge, LA home on July 18, although she last spoke with her family a couple of weeks earlier.
Her husband Oscar Lozada boarded a plane from Dallas to Venezuela July, only with the couple's young daughter.
He was scheduled to return July 14, but it appears he remained in the South American country and while Detectives were able to speak with him early on in the investigation, in the last week he has disappeared.
East Baton Rouge Sheriff's Office spokeswoman Casey Hicks told CNN: "We would obviously like to speak with him," Hicks said.
"Detectives have communicated with Oscar Lozada at the beginning of the investigation into her disappearance, but over the past week, they have been unable to contact him."
She added that no warrants have been issued in connection with the disappearance.
Authorities have examined the husband's credit card statements and found that he bought five-gallon buckets and several bags of concrete mix.
But, Hicks said: "The buckets and concrete mix are unaccounted for."
Walter Lemoine, principal at Brusly High, said Sylviane Finck Lozada had been a West Baton Rouge Parish Teacher of the Year. She is also a National Board Certified Teacher and had earned a doctorate degree two years ago.
Lemoine called Sylviane Finck Lozada a "tough" teacher and said her disappearance is "a major impact" to the community.
On August 8, the 500-student school was scheduled to hold "a celebration of hope" in the gymnasium for the missing teacher, and participants were also to move outdoors to light vigil candles, Lemoine said.