Some of the scenes for the movie starring Michael Fassbender and Marion Cotillard were shot on the island.
The locations included the Storr and the Quiraing, two striking features of the landscape in north east Skye.
Donald MacDonald of Aros, the Portree arts centre with the cinema, hopes to convince distributor Studiocanal to let it show the film next month.
So far Studiocanal has said the movie will not be available to the Aros until a later date.
Mr MacDonald said showing Macbeth on the day of its nationwide release would make it more attractive to audiences.
He said: "If it comes later on people will have lost that initial interest.
"You really want to capture that interest at the time of release."
Mr MacDonald added: "In many ways the small independents need more support than the large cinemas and the multiplexes that can attract large audiences all year round."
Meanwhile, ahead of the new film's UK release on 2 October, VisitScotland has released a guide to sites connected to the real, Shakespearean and Fassbender versions of Macbeth.
The list features the locations on Skye, where the scenes filmed include a large battle scene.
Also on the guide is Dingwall, the town in Ross-shire where it is believed Macbeth was born in or about the year 1005.
Forres - where Shakespeare located King Duncan's castle and near the "blasted heath" where Macbeth had his encounter with the three witches - is mentioned.
Other sites include Cawdor Castle near Nairn, Elgin Cathedral and Glamis Castle in Angus.
The guide was unveiled at an event at Brodie Castle at Brodie in Moray.
Mike Cantlay, chairman of VisitScotland, said: "This new guide gives visitors to Scotland a fascinating insight into one of our most enduring figures.
"Featuring places of historical significance, theatrical intrigue and stunning beauty, our new web pages will encourage more people to discover the places associated with Macbeth - the man, the myth and the legend."
The only permanent cinema on Skye wants to screen the new Macbeth film on the same release date as larger UK cinemas.