The figure, revealed by council officers at a cabinet meeting today, was described as 'unaffordable' by leader Julie Dore.
But after a working group said trees planted to commemorate war dead should be treated differently to other street trees, councillors this afternoon asked for detailed plans to be drawn up show the public exactly how they could be retained - and at what cost.
Twenty-three of the 54 memorial trees in Western Road, Crookes, along with others in streets such as Heathfield Road in Frecheville, were chosen for felling and replacement as part of the 25-year Streets Ahead PFI contract with Amey.
But the council agreed to look again at its plans after a campaign by residents and others against the felling.
A cross-party working group concluded memorial trees should be retained 'where practicable and affordable'. And today the council's head of highway maintenance Steve Robinson said he thought that work could cost about Â£350,000.
In Western Road alone, he said, the figure could come to Â£250,000.
Three of those trees are diseased so need to be felled. But in order to keep the remaining 20, the pavement would need to be built out around them.
This would mean taking away at least three parking spaces per tree.
And it would also mean Western Road becoming a one-way street.
Other issues such as ramping to cover roots, new drains to stop homes flooding and repairs to properties being damaged by roots would also have to be paid for.
Mr Robinson said there were 12 more memorial trees across the city that could not be saved so would need to be felled.
Six could be retained if the pavement were built out, which including the related highway work could cost about Â£100,000.
"That's not a result of a detailed design," said Mr Robinson. "We would have to spend some money to do a detailed design."
Cabinet member for the environment Bryan Lodge said the council did not yet have a plan with detailed costing included that it could show residents of Western Road and other streets. And if work were to take place, councillors agreed that residents would have to be consulted.
"I think the residents in that road need to know what the implications of anything like that might be," Coun Lodge added.
But in a meeting where an Â£18 million social care budget gap was also discussed, he said people could not just 'assume that the funding is available'.
Officers will now work with Amey to come up with potential solutions and costings.
The council confirmed war memorial trees would not be felled while discussions took place - unless they were dangerous, in which case Coun Lodge said he would 'hope people will allow us to deal with that without hindrance'. The council won an injunction stopping people from protesting inside safety barriers earlier this year.
Two members of the Frecheville Community Library group also spoke at today's meeting. Cedric Hinchliffe and Vernon Wallace presented a petition calling for their memorial trees to be saved.
They also urged the council to replace any trees that did need to be felled.
The authority has promised to replace every street tree it cuts down, and also to restore war memorial avenues to their original status, even if that means planting more trees.
It also wants to plant 300 new memorial trees in the city's parks.
The council says felling is always a last resort, but campaigners say trees are being cut down for profit.