ICE campaigners have been told they need to show operators a city rink could be a commercial success on its own because the council will not subsidise one.
The council's finance boss said the council was doing all it can to facilitate the return of a permanent rink to the city after 20 years.
But Councillor Jeremy Moulton said it would be up to developers to make the dream come true.
"If the market is willing to build and run an ice rink all it has to do if find a site and get planning permission," he said.
He was speaking after scores of campaigners marched through Southampton calling on the city council to finally replace the Top Rank ice rink which closed in the city 20 years ago.
They also presented a Daily Echo-backed petition signed by more than 5,000 campaigners also showing their support for a rink.
Cllr Moulton said the Tories had done more than any previous administration to help bring it about, including putting money aside for feasibility work and talks with operators and developers.
But he said council estimates suggested a city centre rink would require a council subsidy of at least £1m which was "unaffordable".
He ruled out selling land cheaply for schemes that offered no guarantees such as a proposed £60m ice rink complex for St Mary's Road.
Cllr Moulton said if the cash-strapped council was to spend money or subsidise a rink frontline line services, such as road repairs, bin collections and social services, would face cuts.
"If we offer subsidises, something else has to give. It's not a top priority when it comes to spending.
"If we get into the habit of underwriting facilities like this, what's next?"
Cllr Moulton said talks with operators and developers suggested a viable commercial rink would have to be part of a larger leisure or retail complex.
He added: "The more that local people can express desire for an ice rink to leisure operators the more chance there is.
"We will continue our dialogues and are doing all everything we can to facilitate a deal."
