The councils are considering a range of options as part of attempts to cut costs and preserve frontline services.
Among the possibilities being put forward are plans to increase the use of joint commissioning across the local authorities and to share a senior children's services management team.
The three councils are compiling a business case that will be voted on by councillors by the end of the year.
Hartlepool acting chief executive officer Nicola Bailey said: “Social care accounts for the biggest spend across the councils and all of us are going to have to make savings over the coming years. Working collaboratively, in commissioning for example, will help bring the costs down.”
She acknowledged that job losses across the departments “were inevitable” but added “we have to bring costs down anyway, so that would happen whether we work more collaboratively or not”.
Bailey said the councils, of which Darlington and Redcar & Cleveland are Labour controlled, already have “close links” politically. Labour is also the largest political group represented on Hartlepool’s council, which has an independent elected mayor.
She added that the councils already work closely on specific aspects of social care and education, such as education support services.
A spokeswoman for Darlington Borough Council confirmed that its cabinet would consider the plans later this year.
Once the councils have approved a set of plans, a public consultation will launch early next year with final proposals set to be approved by the end of March 2013.
Last year Hammersmith & Fulham, Westminster and Kensington & Chelsea councils combined their children’s services departments, overseen by a single director of children’s services. The move is expected to save the three London councils £11.8m a year by 2014/15.