According to reports they are the Department for Work & Pensions and HM Revenue & Customs, the two biggest government users of postal services.
A spokeswoman for the Department for Work & Pensions confirmed that its board was looking at what areas of its operations, which include JobCentre Plus, would be suitable for running a trial.
The report also claimed that HM Revenue & Customs would start a test within weeks, although a spokeman for the department would not confirm this.
"As part of a staged deregulation in the postal market which will be fully deregulated on January 1 2006, we keep all options open. We are constantly looking at new ways for us to communicate with our customers and to reduce our postal spend," the spokesman told the Daily Mail.
The article linked TNT Mail and Business Post with the trials. TNT Mail could not be reached before publication and Business Post refused to comment.
The two have already won large business contracts away from Royal Mail. TNT Mail recently won work from Lloyds, adding to other clients Sky, Caudwell Communications and Booker. Business Post's UK Mail division has added Royal Bank of Scotland to Powergen.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .