Dressed in a suit, he handed out currencies in exchange for sterling to customers at the Asda in Trafford Park, police said.
He then emptied the safe into a bag before walking out of the store at 15:45 BST on 29 July.
Police said they were still searching for the man, described as in his mid 20s or 30s, Asian and of slim build.
A 22-year-old woman has been arrested and bailed on suspicion of conspiracy to defraud.
A man has walked away with £40,000 from a superstore in Manchester after posing as a manager at the Bureau de Change.