Police say the Explosive Ordinance Disposal (EOD) team are en route to investigate the package in Staffordshire.
Stoke-on-Trent Police has said a 100m cordon had been put in place and roads surrounding the store were closed. All roads have now reopened and cordons lifted.
Scotia Road in Stoke was one of the roads closed and the entire length of Willamson Street, which runs between Asda and Matalan, had been cordoned off.
Police were called to the scene at 8:30am (Thursday 22 September).
In a Facebook post published this morning, the force said: "Officers are currently at Asda, in Tunstall, following reports of a suspicious package being found outside the store."
"Police were called at 8.30 am. The store has been evacuated and a 100-metre cordon is in place."
"Roads surrounding the store have been closed, including Scotia Road. The Explosive Ordinance Disposal team are on their way to assess the package."
"Police are appealing for witnesses. Anyone with any information should call the police on 101, quoting incident number 121 of 22 September, or call Crimestoppers, anonymously, on 0800 555111."
In an update, police said: "The cordon has been lifted at Asda in Tunstall after a package was found to be non-suspicious and deemed as no risk to the public."
"Officers attended the scene and a cordon was put in place as a safety precaution."
"The Explosive Ordinance Disposal (EOD) team also attended to assess the package."
"Surrounding roads have now reopened."
"Officers would like to thank members of the public for their patience and support while this incident was dealt with."