The Blackpool Gazette reported that a series of messages had been put on Facebook by a poster it chose not to name, who said he plans to "kill as many people as possible" at the school on Monday in revenge for alleged bullying.
He praised gun killers in schools in the United States and posted: "Nobody talks to me or notices me except when they're calling me a nerd and pushing me around."
When challenged by one student, he asked: "You think it's a joke? You'll see bullets, bodies, and blood."
Principal Tony Nicholson said in a statement to parents and carers: "You may be aware of references on social media from an anonymous source regarding Monday 4th January 2016 at Montgomery High School.
"Staff at the school were quick to spot this posting and the matter was immediately referred by the school to the police. We have been working very closely with Lancashire Police in this regard over the last 48 hours.
"The police have released this statement for us to publish: 'We are aware of the posts and are investigating them but at this time there is nothing to suggest they are credible. Notwithstanding, if the matter is not resolved by Monday, we will ensure an appropriate police response on Monday morning to ensure the safety of all persons in the school'.
"The safety of our pupils and staff is paramount.
"I am in full and constant liaison with the police and have been over the last few days. I can fully assure you that all efforts are being made by both the academy trust and the police to identify the source and nature of the postings.
"We are satisfied that the police are doing everything possible to investigate and protect and they are providing strong support in order to help us to safely open the school as normal on Monday morning."
Police have promised to ensure the safety of everybody at a school which has been threatened on social media.
The principal of Montgomery High School in Bispham, Blackpool, said the safety of pupils and staff is paramount.