Chairman of the Bridge Board Sean Chaytor said they were looking at options including raising barriers, but also at nets.
It comes a decade after the fixed sides of the bridge had 8ft aluminium structures added as part of a pilot scheme.
However a £4.5m scheme to replace the low level railings across the entire width of the bridge with new, higher parapets never materialised.
Speaking following a visit on Thursday by Jackie Doyle Price, Minister for Mental Health, Inequalities and Suicide Prevention, Coun Chaytor said they expected a report to the board in September.
He said: “We are looking at it because we take seriously the issues round the public and public safety.”
Speaking earlier West Hull and Hessle MP Emma Hardy said she recognised the technical difficulties facing the suspension bridge over adding extra barriers, but “to say there is absolutely nothing that can be done - I don’t believe it”.
In recent weeks four new high definition cameras have been installed on the bridge directed on the walkways.
The MP said: “In the past few months they have been taking action, but I would still like them to look at barriers and how we can improve safety that way.”
Ms Doyle Price, who met volunteers from the Humber Rescue lifeboat, which is called out around 120 times a year, said the number of suicides was falling nationally, but added: “We are still losing 13 people a day, that is 13 too many.”
She said there was too much stigma round mental health and people needed to reach out and talk to those who were “visibly struggling” - adding that having a cup of tea could prove a “matter of life or death”.