The trees, believed to be all limes (Tilia sp.), stand on Rustlings Road next to Endcliffe Park in the west of the city.
The council's highways contractor Amey has said they must be felled because they have damaged the pavement, and has undertaken to replace them.
A petition on the change.org site to preserve the trees has nearly reached its target of 1,000 signatures as of today (29 May), while over thirty people attended a meeting of concerned residents on Wednesday (27 May).
Campaigner Deepa Shetty, who launched the petition, said: "Today people were using the pathway with buggies and prams with no issue.
"We request an independent review for these 12 trees and proper consultation with a civil engineer to discuss pavement restructuring solutions."
Amey operations manager for grounds and arboriculture Jeremy Willis said: "The highway has to meet standards according to the Highways Act and so for us to get them up to that standard, there are trees causing that damage which need to be removed.
"We can't not do anything about it – we have a legal responsibility."
In 2012 the city embarked on a 25-year, PFI-funded highways maintenance project across the city, known as Streets Ahead.
Proposal to fell Sheffield street trees prompts residents' campaign
A campaign has been launched to protect 12 mature street trees which Sheffield City Council has slated for felling due to pavement damage.
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