Hartlepool Borough Council's community magazine Hartbeat, could be in line for a £12,000 bonus.
The extra money would allow the magazine to be distributed to homes throughout the borough four times a year.
The Hartlepool Primary Care Trust has offered to provide the money each year to increase the frequency of the magazine.
In exchange for the funding, the trust wants a quarter of each publication to be dedicated to its work.
A spokesman for the council said: "Hartbeat is recognised by the Primary Care Trust as a publication of high quality and credibility.
"Clearly this move would enable the trust to maintain contact with the Hartlepool community in an effective manner."
Discussions are continuing over the sponsorship, which would be for one year initially.
After the first 12 months it has been suggested that the magazine could be funded by the Hartlepool Partnership, to lessen the financial burden on the council.
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