Jan Caszenski, 44, was last seen at his lodgings in Kingsdale Court, Seacroft, on Monday, August 8.
He is described as white with short hair and when he was last seen he was wearing a black jacket, blue jeans and a white T-shirt.
The Polish national had travelled to the city to visit friends, and was due to return to work in Sweden before he went missing.
Police said they are now “increasingly concerned” for his welfare.
Anyone with information is asked to call 101.