Current town clerk Arden Bhattacharya is head of legal services and administration.
The systems organisation development officer post, held by Steve Gillions, may also be scrapped.
The council proposes replacing it with a borough support services officer in charge of administration, information technology and human resources. Leader Geoff Cutting said both the new jobs would be subject to open recruitment.
'This reorganisation will modernise the council and bring us into line with others. Town clerks have been outdated for some time. 'It will bring a strategic focus which is needed for white collar CCT, reorganisation and charter initiatives', said Mr Cutting.
'We wanted to sharpen up our act, get the focus right and get our most senior officers really driving through the changes necessary without throwing the whole lot up in the air'.
The initial idea to create the chief executive post came from the Labour group leadership but PA Consulting Group was then commissioned to report on the implications for the rest of the council.
The consultation process is due to end on 30 September and Mr Cutting hopes reorganisation will be implemented by the end of the year. Mr Bhattacharya declined to comment until after a meeting with the leader next week.