Southampton's second 13-mile event was held on Sunday and attracted more than 6,000 runners.
Race director Chris Rees said there was "definitely a demand" for a 26.2-mile (42km) run at next year's event and one could be formally announced by the autumn.
More than 500 people responded to the suggestion on social media, he added.
Southampton City Council has said it cannot "offer any comment at this early stage", but added it was "delighted" by the recent successes of the half marathon.
The inaugural Southampton half-marathon was held last April, along a route that passes many of the city's landmarks, including the Bargate, St Mary's Stadium and Itchen Bridge.
Organisers said most people who had responded to the suggestion of a full marathon favoured a separate 26-mile route, rather than the idea of running the 13-mile route twice.
Mr Rees said: "This weekend showed how much the city embraces and enjoys running so it would be great to have a marathon in the city - it just has to be done right.
"We've got a couple of ideas and proposals and we want to work with the council, runners and community groups and residents to make sure they are all backing the event."
Organisers of the Southampton half marathon have said they would like to introduce a full marathon to the city.