U.K. Thang, who was found dead at the scene of the shooting last Thursday, had moved to the town of Collierville, around 36km (22 miles) east of Memphis, last summer before starting work at a Kroger.
The local police department, in an update on Monday into its investigation, said he had been “asked to leave his job” as a “third party vendor” before carrying out the shooting. It was not clear why.
Police were called to the supermarket at 1.30pm to reports of a shooting incident on Thursday, to find 14 people wounded and one individual deceased.
The shooter was also fatally wounded, having allegedly turned the gun on himself.
Ten Kroger workers where thought to have been shot by Mr Thang, and four shoppers, including Olivia King, was killed.
According to CNN, four people remain in a stable condition at Regional One Hospital in Memphis,
Kroger customers, as well as staff, recalled hiding from Mr Thang in freezers, while others locked themselves inside an office to escape the alleged shooter.
Glenda McDonald, a Kroger employee, told WHBQ-TV: “I was walking back towards the floral department and I heard a gunshot. It sounded like it was coming from the deli. And I ran out the front door and they had already shot the front door.”
A customer, Jason Lusk, told reporters he had heard 10 to 15 rounds of fire inside the store, and that people were screaming in the car park about a shooter.
He told The Associated Press: “As the firing started, I dove in front of my vehicle onto the ground to provide the most cover for myself and instructed the people around me panicking, trying to get into the cars, not to get in their cars, but to actually hide”.
A SWAT team arrived at the scene within minutes and took control of the situation, finding the alleged shooter with an apparently self inflicted wound.
Collierville police said on Monday that an investigation is ongoing, and that a decision is due to be made on reopening the store.