Political parties have been given until Monday by the British Government to try and reach agreement after they failed to meet Thursday's deadline to strike a deal to restore a power-sharing government in Northern Ireland.
The DUP and Sinn Féin have remained at loggerheads over key issues like introducing an Irish Language Act and same-sex marriage.
Power-sharing talks in Northern Ireland look set to be parked for the summer, with Sinn Féin acknowledging a deal will not materialise before the autumn.
Party sources said they expect the UK and Irish governments to suspend the negotiations, potentially later today, with the aim of restarting the process in a number of months.
Discussions continued inside Stormont Castle on Tuesday, but no substantive progress was made.
The DUP and Sinn Féin, the two parties whose sign-off is required to form a devolved government, remain at loggerheads over a range of issues.
Sticking points include the shape of legislation to protect Irish language speakers, the DUP's opposition to lifting the region's ban on same-sex marriage, and mechanisms to deal with the legacy of the Troubles.
Earlier, Irish foreign minister Simon Coveney said if a breakthrough did not come on Tuesday then one would not be forthcoming on this side of the summer recess.
The assembly's official summer recess starts on Friday.
Prime Minister Theresa May has met with the leaders of the DUP and Sinn Féin in an attempt to revive efforts to get Stormont up and running.
An emergency move to ensure funding for vital public services in NI does not run out has cleared its final parliamentary hurdle.
Prime Minister Theresa May has urged the DUP and Sinn Féin to “bridge the gaps” on outstanding issues fuelling NI's political stalemate.