The plans are outlined in a leaked internal email by Border Agency director of comms Rob Yeldham on 26 March.
The email states that, as a result of Home Office permanent secretary Helen Ghosh creating a smaller policy unit, the UK Border Agency's strategic border and immigration policy role will be transferred into the core Home Office.
To support this, from April, the agency is changing how it provides comms support on border and immigration issues.
Yeldham wrote: 'We are moving to a model where different comms functions are provided on a shared service basis by either ourselves or the Home Office. Some services will remain separate. These changes largely affect how we manage our delivery channels.'
Yeldham added that his directorate will now be responsible for strategic comms and partner engagement around border and immigration issues for both the agency and the Home Office itself.
He said the changes should be 'indiscernible to partners working in the comms and stakeholder engagement fields'.
A Home Office spokesman said: 'We want to provide better value for money and the changes in how we are organised will ensure that comms is done once, well and in one place wherever practical.
'Rather than assuming everything should be done by one agency or unit, we are quite deliberately looking for the best place for specific functions to live. This will help us build efficiently on different areas of expertise and capability across the Home Office and its agencies.'