The Forum 18 news service claims that because the region is now under control from Moscow it means religious leaders need to meet Russian laws.
That means Ukrainian priests must register as 'foreign' leaders or leave.
The news agency says it has found no proof that any priest has registered so far.
Crimea was part of Ukraine until March 2014 when Russia decided to annex the region after a revolution in Kiev.
Forum 18 claims to have asked a Russian immigration official about the rules.
It said he replied: "I don't know. It's not my problem."