Recent political agreements in Northern Ireland have essentially been negotiated between the DUP and Sinn Fein.
"I am very reassured by what the prime minister said to me today that that won't be the case".
Mr Coveney met all five main political parties and Secretary of State James Brokenshire in what was his first involvement in the process since replacing Charlie Flanagan at the head of the Department of Foreign Affairs in Dublin last week.
The parties have until 29 June to reach agreement and have been warned that if they cannot, direct rule could follow.
"For the EU27's part, we have set out our position plainly and in this position there is a strong acknowledgement of Ireland's unique concerns and priorities, including on: protecting both the Good Friday Agreement in all its parts and the gains of the peace process; avoiding a hard border on the island of Ireland and; maintaining the Common Travel Area", he said.
"All of the messaging I am getting is people are up for a deal", he said.
A DUP source confirmed negotiations were "ongoing" and said they were looking to deliver "a more compassionate style of government for the whole of the UK".
"As a UK Government we remain absolutely steadfast in our commitment to the Belfast Agreement, its successor agreements".
Northern Ireland has been without a powersharing Executive since March and without a first and deputy first minister since January.
The institutions collapsed amid a bitter row between the DUP and Sinn Féin about a botched green energy scheme.
"We continue our discussions with the DUP".
He added: "We see no reason why devolution and the executive can't be up and running now".
The Irish foreign minister said an agreement should not be an accord struck only between the two largest parties - the DUP and Sinn Fein.
Asked if the Brexit process increased the pressure on her party to re-establish an Executive, Mrs O'Neill said Sinn Féin was already making the case across Europe for Northern Ireland to retain special designated European Union status.