Speaking outside Parliament in London after the British Irish Intergovernmental Conference, the Tanaiste said a no-deal Brexit is not in British or Irish best interests, but he remains confident a deal will be reached.
Mr Coveney said the negative implications of a no deal Brexit are "very significant for Ireland and for the UK".
Mr Sewing added the German bank will be prepared for any outcome of the Brexit negotiations between the United Kingdom and the EU.
He dismissed suggestions that amendments to Brexit legislation forced on Mrs May by Eurosceptic backbenchers would prevent agreement on a "backstop" arrangement for the Northern Irish border.
Speaking to the Today programme Mr Coveney described talk of the United Kingdom "crashing out of the EU" as "bravado".
On Tuesday, the PM confirmed that as the Brexit talks entered their final weeks she was taking personal charge of them with Mr Raab "deputising" for her in Brussels.
Tory Eurosceptics have voiced concerns that Mr Raab's department has been sidelined by Number 10 and Mrs May's Europe adviser Olly Robbins, amid increasing speculation that divisions within the Conservative camp may result in a no-deal Brexit.
"This sends a very clear signal that Britain and Ireland are going to remain very close, regardless of the challenges we face".
"But we are not talking about devolved decision-making in Northern Ireland today, we are talking about the structures that can enable a functioning executive there that can bring normality back to Northern Irish politics".
"But I think, even though the timetable is tight, it is possible to achieve an outcome that is good for Britain and good for the European Union within the timelines that are now there".
He said: "We need to be focusing on the intensification of negotiations to try and find the solutions on a way forward as opposed to the sort of tough stance that some people feel the need to take in relation to saying "well do your worst, we can deal with a (no-deal) situation".
Mr Hammond also ruled out extending the Article 50 process to give more time to negotiate withdrawal from the European Union, after the Irish Government said it would back such a move.
"We now have clarity in terms of what the British Government ask is", he said.
He told MPs in the Exiting the EU Committee: "I don't doubt that we would have to look at the uncertainty that we would face in the short-term, but I think long-term actually we would still be able to thrive".
Michelle O'Neill said both the British and Irish governments have a responsibility to ensure the Good Friday Agreement is implemented.
A key focus for the country is to create a legally operable backstop, keeping Irelands borders open with the United Kingdom, particularly with the landlocked Northern Ireland.
However, unionists have been critical of the conference, with former Northern Ireland first minister Lord Trimble accusing Dublin of "meddling".