The 1,743sq.m shop which will create up to 50 new jobs, is on the site of the former Bay Leaf restaurant which closed in 2007.
Although Aldi have not confirmed the opening date, a May deadline has previously been reported.
Builders are currently working on the site, with a two-storey metal frame now in place, earthworks being carried out and a new entrance formed.
Aldi has been planning to build on the site since 2018 , but after gaining approval in March 2020, it was taken to the High Court by rival supermarket chain the Co-operative Group.
Objections included that the land was designated as Green Belt, proposals had previously been identified as being "harmful to openness", and that an Aldi supermarket would cause a a significant adverse impact on the vitality and viability of the village centres of Tarleton and Hesketh Bank.
The case was eventually thrown out, and final approval for a slightly amended application was approved in April 2021.
>>>Click here to read more about the wrangle to get permission for the store.
Letters of support were also received for the application, saying it would tidy up the site, give shoppers more choice and create more jobs locally.
Five jobs for the store are currently being advertised on recruitment website Indeed.com.
They include store assistant (£10.10 per hour), stock assistant (£9.90 per hour), apprentice (£6.61 per hour), caretaker/cleaner (£9.90 per hour) and deputy manager (£11.10 per hour).
Aldi has been approached for comment.