State media in the Gulf kingdom said a request had been made by Danish Foreign Minister Villy Soevndal, citing the prisoner's Danish citizenship.
Human rights organisations have called for Mr Khawaja to be freed.
His daughter Zainab has been protesting over her father's worsening condition.
Having been arrested on Thursday at a rally, she was released on Saturday but vowed to continue her campaign for her father's release.
Mr Khawaja has been moved to a hospital clinic and is being fed intravenously after 58 days on hunger strike.
He is protesting against a life sentence he received for his role in anti-government protests by Bahrain's Shia Muslim majority last year.
A special security court convicted him of trying to overthrow Bahrain's royal family, who are Sunni Muslims.
The Danish request has been referred to the head of Bahrain's supreme judicial council who is due "to study it and make a decision", Bahrain's state news agency reported.
Security forces fired tear gas and water cannon at thousands of protesters who rallied in support of Mr Khawaja on Friday.
Many were carrying posters of him as they called for his release.
Other protests have also been held in recent weeks against the motor racing Grand Prix which is due to be held in Bahrain later this month.
Zainab Khawaja was arrested on Thursday at a rally outside the interior ministry, where she was accused of "assaulting a public employee".
After questioning, she was freed on Saturday but is said to have tried to gain access to the hospital where her father is being treated.
On her Twitter account, she said her father had phoned the family and could "hardly speak... hardly breathe".
"My Dad said he will not stop his hunger strike and told guards 'If I die, I die with dignity'," she wrote.
"My mother told my Dad that we all support him, that we're proud. We are with him all the way, no matter what he decide[s]."
Human rights group Amnesty International says Mr Khawaja's conviction in June was based on a confession made under duress, and no evidence was presented showing he had used, or advocated violence, during the mass protests early last year.
Bahrain is considering a request from Denmark to transfer political prisoner Abdulhadi al-Khawaja, who has been on hunger strike for almost two months.