The Alberta mother who drowned her two young boys three years ago could be released from custody as early as Thursday. 

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Curtis and Allyson McConnell are shown with sons Connor and Jayden in an undated photo. (Facebook)

Allyson McConnell, 33, has been in Alberta Hospital since she was convicted of manslaughter in April 2012 in the deaths of her two sons, 2½-year-old Connor and 10-month-old Jayden, in February 2010 at their Millet, Alta., home during a divorce battle with her husband.

She left their bodies in the bathtub to be discovered by her husband before trying to kill herself by jumping off an overpass.

She was sentenced last June to six years in prison, which left her eligible for parole last month after receiving two-for-one credit for time already served.

The sentencing judge recommended McConnell, who is still believed to be suicidal, remain at Alberta Hospital until she's no longer a danger to herself or others.

As McConnell is an Australian citizen, her lawyer has been trying to pave the way for her to return to her family.

McConnell is under a removal order issued by the Immigration and Refugee Board of Canada, said Lisa White, spokesperson for the Canada Border Services Agency.

The agency is required to begin the deportation process once a foreign national is convicted of a criminal offence, she said.

Alberta's justice minister wants McConnell to stay in the country until the Crown's appeals on the length of her sentence and the manslaughter conviction are heard, but White said an appeal cannot stop McConnell's extradition.

"Our laws state that Canada Border Services Agency must enforce the removal order as soon as is practicable," White said. "By law, a criminal appeal of conviction does not stay a removal from Canada."

However, as a last resort the province can ask the federal court to stay McConnell's deportation.

During the trial, the prosecution argued McConnell killed the boys as revenge against her husband, who had refused permission to let her return to her native Australia with the boys.

However, the defence said the fact McConnell suffered from severe depression coupled with her use of alcohol and sleeping pills meant she could not have formed the intent required to convict her of second-degree murder.

With files from CBC's Janice Johnston