The council is looking to appoint an agency to outsource its corporate press office work on a three-year contact.
A decision is expected by the end of this week.
Eastbourne currently uses locally based Cobb PR to handle an element of its press office, although the new brief will outsource the council's entire corporate PR. Cobb has pitched for the new brief.
Eastbourne head of strategy and democracy Peter Finnis said: 'It was decided to close down the internal element, so we're out to tender for a combination of high-level corporate PR and outsourced press office.'
Finnis said the £140,000 budget came in at £30,000 cheaper than paying for the in-house press office.
The deadline for tenders has now closed.