Atos issued a statement saying it has been discussing an early exit from the £500 million contract with the Government for “several months”.
The provider confirmed it would not stop delivering the service until a new provider was appointed.
The news follows reports in the Financial Times that Atos recorded more than 160 incidents of abuse on its employees each month in 2013.
Atos centres have been the focus of several protests against work capability assessments, which the Government introduced to determine who should receive employment and support allowance.
In July last year, the Department for Work and Pensions announced Atos has been instructed to enact a quality improvement plan, after results provided by the company showed a reduction in quality.
The statement issued by Atos in relation to its contract said: "For several months now, we have been endeavouring to agree an early exit from the work capability assessment contract, which is due to expire in August 2015.
"Despite these ongoing discussions, we will not walk away from a front-line service. Our total focus remains on delivering the services we are contracted to provide in a professional and compassionate way until a new service begins."
A blog posted by Atos last week urged protesters not to blame Atos staff for Government policy decisions.
“We maintain at all times the right of our staff to work without intimidation or threat,” it said. “Please remember our staff do not set policy. They should not be targeted personally for things outside of their control.”