A report to the joint senior staff committee said the current salary of £125,406 would be unlikely to attract candidates of a high enough calibre to deliver on the ambitions of the two councils.
The committee recommended that the new salary should range from £134,000 rising to £155,000.
With pension contributions and National Insurance on top of the salary, that will take the cost to £176,860 at the lower end of the scale and £204,780 at the higher end.
At the moment, the interim CEO is Dr Catherine Howe, former director of communities, who stepped into the top role after Alex Bailey announced his retirement.
Recruitment of a permanent CEO is expected to start in September or October – a process which is likely to cost around £30,000.
Sharing advice from local government specialists SOLACE, the report added: “SOLACE have indicated that the current salary would be unlikely to be sufficient to attract a high calibre, diverse pool of candidates with the depth of experience, track record and/or capability to match and deliver the councils’ ambitious agendas.”
Approval for any salary increase will have to be given by the full councils, both of which will meet later this month.