Proposals are currently being assessed by the Planning Service, which is expected to return its decision before Christmas.
The £25m development on the Ballymena Road could create up to 400 full and part time jobs.
Asda has said it will use all local contractors to construct the 54,000 square foot store, which would provide many much-needed jobs in the industry.
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Plans were originally lodged in 2006, for what would be the chain's largest Northern Ireland store.
According to the supermarket's Property Manager, Philip Bartram, construction at the site could last up to eight months.
Mr Bartram said: "We are working closely with the Planning Service and are hopeful of a swift decision on our plans.
"People of Antrim want supermarket choice and they want to see an Asda store at Junction One as soon as possible. They deserve a decision by Christmas."
A spokesman for the Planning Service said: "We can confirm that the application is still under consideration."
Asda moved into the Northern Ireland market over three years ago, as part of a takeover of 13 Safeway store.
(PR/JM)
