Powersharing has been in deep freeze since early this year when the late Sinn Fein deputy first minister Mr McGuinness resigned in protest at the DUP's handling of a botched green energy scheme which risks landing the taxpayer in millions of pounds of debt.
"Northern Ireland simply can not continue without democratic oversight and that means the speedy introduction of direct rule if agreement is not reached".
The Creggan councillor said: "RTÉ reports that Jeffrey Donaldson "gave the example of Sinn Féin wanting 10 per cent of all public jobs to go to Irish speakers".
She described it as a "common-sense solution" to the political deadlock. "We are open to that if it helps to develop the process", she said.
The party said restoring government in Northern Ireland under the current circumstances would only lead to another collapse.
"We also agree to bring forward legislation to address culture and language issues in Northern Ireland within a time-limited period to be agreed".
"If we are to have an agreement then there will need to be a willingness on all sides to reach out in order to secure a durable outcome", she said.
"The statement by the DUP leader demonstrates that they have not listened or acknowledged the reasons of Martin's resignation". They have failed to deliver people their rights.
"Let's agree to quickly conclude talks on implementation and rights, that is the only way to build a sustainable Executive that will last".
Sinn Féin's rejected the idea, saying it doesn't trust the DUP to stick to its word.
Irish nationalists Sinn Fein must compromise if Northern Ireland is to avoid a "speedy" return to direct rule from London, the head of the Democratic Unionist Party said on Thursday.