A force spokesman said the two men were described as Asian and wearing dark clothing.
The spokesman said: "We were called by a farm owner at about 11.30am on Wednesday who said that one of their workers had interrupted two males killing a sheep from their flock.
"Officers attended the scene at about 2.10pm and spoke with the farmer who believed they had entered the field and killed one of the sheep.
"The men are described as Asian and wearing dark clothing.
"Anyone with any information should message Staffordshire Police on Facebook or Twitter quoting incident number 249 of February 3, or alternatively contact Crimestoppers anonymously on 0800 555 111."