Both NHS East Riding and NHS Hull have been told to slash management costs by 43 per cent.
A total of 250 letters have been sent to managers and administrators at NHS East Riding, inviting them to take voluntary redundancy or early retirement as it seeks to cut costs by 4m.
NHS Hull said it would write to its entire workforce of 300 staff next week, and it is expected this will include a similar offer.
The East Riding trust said it does not have a target number of jobs it needs to shed, and that the cost-cutting measure would not affect clinical staff. But it could not rule out compulsory redundancies.
Chief executive Ivan Ellul said: "Under the terms of the NHS operating framework, along with all Primary Care Trusts nationally, we are required to make management savings.
"For NHS East Riding of Yorkshire we have to make management savings of over 40 per cent to invest back into local health care services by 2013-14.
"Our management budget for 2010-11 is 8.6m which equates to 1.8 per cent of our current budget of 487m.
"We are currently considering a whole range of measures, including inviting expressions of interest in voluntary redundancy or early retirement."
The offer will be open for six weeks.
The area organiser for public sector union Unison, Karen Towner, said: "It's not a surprise. We are going to be working with the trust to try to make this as painless as possible.
"We will be giving our members the advice and support we can but it's not the trust that has made the decision, it's Government policy."
The trust currently employs 1,300 people, although the 1,100 who work in community services are due to transfer to Humber Foundation Trust in March next year.
NHS Hull said it had until April 2014 to bring about the management savings.
A spokeswoman said: "We are currently drawing up plans for how this might be done, but we do not anticipate any compulsory redundancies in the current financial year, 2010/11."
NHS Hull employs around 300 staff in areas such as finance, commissioning, public health and patient and public engagement.