Impulse Leisure asked the council for support in order to keep its local arm, Adur Community Leisure, trading during the coronavirus lockdown.
But a council spokesman said the council considers the company's recover plan to be 'lacking in detail and insufficiently robust', adding the company's instability and stretched public funds made a loan too risky.
The leisure company had warned that 154 jobs would be lost if its Adur centres collapsed and its Worthing and Storrington branches could follow.Councillor Emma Evans, Adur District Council’s cabinet member for the environment, said the council understood how devastating the news must be to staff during these uncertain times.
"We will do all we can to try to reopen those centres as soon as is practicable," she said.
"Obviously these are difficult times for many businesses and leisure centres are no exception. The council has done everything possible to support Impulse moving forward. But we also have a duty to local taxpayers to ensure that local services are operated efficiently and cannot place a large financial burden on the authority to prop up an external organisation.
"But we believe there is a solid future for these centres if we can find the right operator. The lockdown has proved that people are looking to become more active and if we can look imaginatively at future offerings I see no reason why we can’t return these centres to full health at the heart of their communities, with a more robust community based leisure arrangement."
The leisure centres to be immediately affected are Lancing Manor Leisure Centre, Southwick Leisure Centre and Waders Community Pool in Shoreham, which are all owned by Adur District Council.
Impulse Leisure also runs The Gym Hub in Worthing's Guildbourne Centre and Storrington Leisure Centre.
The council awarded Impulse a 30-year contract in 2005 to run its Adur leisure centres. It is registered as a charitable trust and any financial surplus goes to the company, not the council, and the council pays an annual service fee to Adur Community Leisure to deliver the services.
All of its centres have been closed since late March due to the coronavirus lockdown.
A council spokesman said there was 'ongoing concern' about how the company would finance itself in future, which made it unable to offer the large one-off payment requested by Impulse as it was not clear how it would be paid back.
The council had paid the full annual service fee in advance, the spokesman said, but its own finances had also been badly affected by the lockdown.
"The Council believes it could have a good opportunity to reboot the leisure centres post-pandemic with new operators to meet the rising and changing needs of residents to leisure and wellbeing activities," the spokesman said.
"Members will make a final decision at Adur & Worthing Councils’ Joint Strategic Committee on July 7."