Tom Evans and Kate James had hoped to persuade appeal court judges that their 23-month-old son Alfie should receive life-support treatment overseas.
Thomas Evans, 21, and Kate James, 20, will find out on Monday if the Appeals Court will overturn the High Court ruling and allow them to take their ill son to a hospital in Italy for treatment, reports The Mirror.
But his parents disagreed and said they wanted permission to fly him to the Bambini Gesu Hospital in Rome for treatment.
The court ruled that his life support won't be turned off until the Supreme Court has reached its decision.
Merseyside Police has confirmed last night's protest on behalf of Alfie Evans took place peacefully and thanked the toddler's family for the reassurance they offered to the crowd that gathered to support them.
Roger Kiska, legal counsel at Christian Legal Centre, told CBN News last week the parents have the legal right to remove Alfie from Alder Hey Children's Hospital.
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He then alleged the hospital called the police to prevent him removing his son, with officers allegedly telling him he would be "arrested for assault" if he attempted to remove Alfie.
"Their views and rights do not take precedence and do not give them the choice to make the decisions regarding Alfie", he stated, the news outlet reported.
In the early hours of this morning, the force confirmed it was present while clarity was sought over Alfie's care with the judge who had overseen previous court hearings on his future. "It is precisely because of this judicial determination that Aflie has been kept in Alder Hey Hospital", Moylan said. "In our view the arguments advanced on behalf of the parents provide no basis on which Alfie could be said to be detained, or on which he could to be said to be unlawfully detained", Moylan said, according to Liverpool Echo. Courts have refused to allow the parents to determine what is in Alfie's best interest.
"Alfie, the family and all of our supporters are stronger than ever".
Supreme Court justices and European Court of Human Rights judges have refused to intervene.
The toddler is battling an undiagnosed brain disease, according to reports. Supporters have since demonstrated outside the hospital and bosses have pleaded with those assembled not to disturb staff or patients.