The guard, identified as Angelica Magdici, 32, enabled convicted rapist Hassan Kiko, 27, to break free from the Limmattal prison on Monday night, Zurich cantonal police said.
Police believe the pair left in a black BMW X1 station wagon with the licence plate ZH 528 411, headed for Italy.
On Wednesday investigators disclosed no further information, saying they were pursuing “various investigative steps”.
But Magdici's husband told 20 Minuten newspaper he did not believe the pair were going to Italy.
“I think they are on the road to Syria,” the 25-year-old husband of the prison guard said.
The couple married in 2014 but have been separated for the past three months.
The guard's husband told 20 Minuten that he had noticed his wife had changed a lot recently.
She had started to read the Koran and become very interested in Syria, he said.
“I think she has also become a Muslim.”
The husband said the pair drove off in a car that he part-owned, so he filed a complaint with police on Wednesday.
Kiko told the Thurgauer Tagblatt in 2011 that he fled Syria after being imprisoned for three months by the Assad regime.
A photo posted to Facebook shows him posing in the gym, displaying a body builder's torso with tattoos covering his right arm.
He had worked as a hairdresser before being convicted of rape and sentenced to four years in jail, 20 Minuten said.
Facebook photo of Hassan Kiko in the gym. Photo: Zurich cantonal police