The authority believes the byelaw would be the first of the kind in the country.
A deal struck between the shopping centre and the council in 1977 means that, unlike most shopping centres in the country, Eldon Square's walkways are treated like normal streets by the council - prompting the need for the byelaw.
Centre operations manager Malcolm Lumsden said that most of CSC's centres had no-smoking policies but Eldon Square was different in that it needed a byelaw.
The MetroCentre in Gateshead, also owned by CSC, will become no smoking on January 5 - but no byelaw has been applied there.
A report to Newcastle City Council's constitutional committee, which meets today, states that: "We would not be following a precedent for this byelaw.