Social Development Minister Margaret Ritchie has spoken to the head of the decommissioning body about progress on UDA arms.
The UDA said it would decommission in its own time
A deadline for the paramilitary organisation to begin giving up guns expires at midnight.
Ms Ritchie has threatened to withdraw more than £1m of funding for a loyalist project if the UDA does not cooperate.
The US government has issued a statement welcoming moves by the UDA to engage with the arms body.
US Special Envoy for Northern Ireland Paula Dobriansky said: "We have consistently called for all paramilitary groups in Northern Ireland to decommission and there is no rationale for the continued possession of illegal arms.
"We are encouraged that interlocutors have now been appointed and hope further negotiations will bring about significant and rapid progress".
Margaret Ritchie says the UDA must decommission its arms
At the weekend, Secretary Shaun Woodward said the paramilitaries had begun "meaningful" talks with the decommissioning body.
The BBC has now learned that Ms Ritchie has talked to General John de Chastelain, the head of the arms body, to get an update on any moves by the UDA to hand over guns.
Frankie Gallagher, of the Ulster Political Research Group, has said Ms Ritchie's deadline could lead to a "disastrous place".
Ms Ritchie said she had come under pressure from direct rule ministers to compromise on her 60-day deadline.
However, Security Minister Paul Goggins said the final decision on whether to redirect £1.2m from the Conflict Transformation Initiative to other loyalist projects was hers.
The UDA said it was adhering to its own timetable for getting rid of its weapons, despite Tuesday's deadline.
The funding was intended to help move the UDA away from violence.