Epping Forest District Council has asked for permission to take its case against a hotel housing asylum seekers to the Supreme Court.
Thousands of people have protested outside The Bell Hotel in Epping over the last two months.
The district council obtained a temporary injunction from the High Court which would have forced 138 asylum seekers to leave by 12 September.
The Court of Appeal overturned the ruling last week. The council confirmed on Monday it had taken the next steps to appealing the decision.
A council spokesperson said: “Indicating our intention to appeal does not commit us to further action but facilitates the later process, should we decide to do so.
“Refusal of the Court of Appeal to allow our request would not close our opportunity. The council would still have the right to apply directly to the Supreme Court.”