When using GRE tunnel for site A to site B connections, is it always necessary that the differents sites belong to separate network segments.

Here is my scenario.

I have two sites which were originally connected by trunk links.

Both sites have identical VLANs but for some reasons site A and site b can no longer use the trunk links.

There is an internet connection on both sites. I am thinking of using GRE to connect both sites but I use to think GRE works easily when site A and site B belong to different network segments.

May be i am wrong. Any ideas on how i can handle this situation will be appreciated.