Immigration Minister Peter Dutton says he and other conservative colleagues are working to find a "sensible" way forward to resolve the issue of same-sex marriage in this term of Parliament.

In an interview on Thursday, Mr Dutton confirmed a Fairfax Media report he was pushing for a postal vote plebiscite as a way to progress the issue without breaking the Coalition's election commitments.

Treasurer Scott Morrison and Finance Minister Mathias Cormann have also privately backed the postal vote idea.

"Lots of us are working together to find a sensible approach through this Parliament," Mr Dutton told 2GB radio.