It comes after Cannock's managing director resigned in February.
The proposals, set to be discussed by Stafford councillors on Monday, would see Stafford boss Tim Clegg take up a dual role.
He would be appointed joint chief executive for an initial 14-month period from June – enabling a "smooth handover" with the interim managing director at Cannock Chase.
Stafford Borough Council leader Councillor Patrick Farrington said the proposals would allow both local authorities to look at further collaboration – in a bid to help make savings and efficiencies across their services.
"We want to ensure our council is more resilient, flexible and sustainable into the future and closer collaboration with our neighbours is a fundamental way in which we can do this," he said.
"Sharing resources has allowed us to maintain, and improve, our services to our residents and businesses as well as making savings for the local taxpayer. But it also ensures Stafford Borough Council maintains its individual identity."
The councils have already shared a number of back-office services for more than a decade – including finance, human resources and legal services.
Councillors in Stafford will hear that during the 14-month period an interim report will be drawn up to evaluate the potential for sharing more services and continuing the arrangements for a joint chief executive between the councils in the future.