Proposals have been submitted to Hartlepool Borough Council planning department to improve the existing click and collect facilities at the Marina Way supermarket.
The existing collection point will be replaced with three new click and collect bays and extra space for delivery vans, which will mean "improved home shopping capacity”.
The service provides the option for customers to shop online and either collect their shopping from the car park or have it delivered to their homes.
It became more popular at supermarkets nationwide following the outbreak of the pandemic last year.
A design and access statement, submitted by C and A Design on behalf of Asda, states the Hartlepool proposals will benefit customers.
It said: "Its installation will improve customer experience and speed of service by introducing a drive thru service.
"The application seeks to improve on Asda’s existing commitment to its ‘home shopping’ service which provides for customers to shop online.
"The increased provision is to meet both current and future demand for the home shopping offer."
The statement adds the operation will have "minimal impact" on the existing Asda site or neighbouring uses.
The development would lead to minor car parking adjustments, with a loss of four car parking spaces overall, according to planning documents.
It would also see the existing home delivery van canopy at the site extended.
A decision is expected to be made on the proposals by the council planning department next month.