Sir Jeffrey held video talks with Ms Truss on Tuesday afternoon. Sources close to the Foreign Secretary denied she had been told to trigger Article 16 in the call.
Ms Truss has repeatedly insisted that her appointment will bring no change in approach and that Article 16 remains on the table.
She will accept some role for EU judges in Northern Ireland even though she insists the UK should not appear before the European Court of Justice in the case of disputes with the bloc.
The Conservatives are no longer dependent on DUP votes since Boris Johnson’s election victory in 2019 brought a large majority. But a drop in support for the DUP in Northern Ireland over the protocol could strengthen calls for Irish reunification.
The DUP is lagging behind Sinn Fein as the largest party in Northern Ireland, according to a November poll by the University of Liverpool, which found they had lost a third of votes received in the 2019 elections.
The DUP has just one seat more than Sinn Fein, which favours Irish reunification, in the current Stormont Assembly. The poll showed almost two thirds of those asked felt it had handled the protocol issue poorly.
There are fears the DUP, which campaigned for Brexit, could be toppled as Northern Ireland’s largest party in Stormont. If Sinn Fein builds on recent electoral successes in Ireland, it could mean governments in both countries being led by the nationalist party.