Film fan Michael Holt and friends came up with the idea as a way of paying tribute to the film's director.
The idea was raised by Mr Holt at Hartlepool Borough Council's last full meeting.
He said he hoped more people would join the campaign. A petition has so far attracted almost 900 signatures.
Mr Holt said: "We're all big fans of Ridley Scott and his films - Alien, Blade Runner, Gladiator and of course Boy and Bicycle that was filmed in Hartlepool, his first film.
"We liked the idea of having a statue or a tribute to him and we were thinking 'what would be the best thing to do for?' and the idea of the alien came up.
"It seemed so surreal and unusual a thing to have as a local statue that we were quite keen to get the idea out there and it seems to have been a success with people," Mr Holt said.
It is hoped the statue would be placed near to the Cleveland College of Art and Design or the Hartlepool College of Further Education.
Kevin Cranney, chair of Hartlepool Council's regeneration services committee, said he would be happy to meet the group behind the campaign but thought it would be "appropriate" to honour Ridley Scott and his late brother Tony, as both studied in the town.
He said: "I think it is a good idea given the council's plans for Church Street and also the investment going into Cleveland College of Art and Design. However, I think we need to look at this in more detail."
The council has received a Â£1.2m Heritage Lottery Fund (HLF) grant to revamp the Church Street area, which will be aimed at raising awareness of the history and heritage of the town.
"I thought they [the council] were going to say 'that's an absolutely stupid idea, don't bother', but they were quite interested in it and I'm going to have a meeting with them soon to see how viable it is," Mr Holt said.
"It would be an inspiration to aspiring film makers."
A campaign is under way to get a statue of the alien from the film erected in Hartlepool in honour of Sir Ridley Scott, who studied in the town.