Dariusz Nowak, a spokesman for police in Krakow, which is 80km from the Auschwitz museum, did not say why investigators were looking at that possibility but added that "indeed it looks like someone is behind it."
Polish media have reported, without citing any sources, that a person living in Sweden could be under suspicion.
Nowak said foreign police have been notified and were working on the case but refused to elaborate.
Police found the sign - cut into three pieces - on Monday, and arrested five suspects in northern Poland.
Three of the five men have confessed to the pre-dawn theft of the sign, which is a symbol of Nazi Germany atrocities during World War II.
Prosecutor Piotr Kosmaty said the three who had confessed were taken back to Auschwitz to show investigators how they unscrewed and tore the 5m-long sign, which weighs 30kg, from the gateposts.
Kosmaty said later that the re-enactment gave police some insights, but did not elaborate.
In Krakow, police displayed the broken sign for journalists. It was cut into three parts, with each part bearing one of the words. Some of the steel pipe that formed its outline was bent and the letter "i" was missing from the word "Frei" because it had been left behind during the theft. It was recovered at the scene.
Police forensics expert Lidia Puchacz said that cutting and sawing tools used in the theft were found at the home of one of the suspects.
