Brexit: Arlene Foster and Martin McGuinness to talk to David Davis
The new minister charged with navigating the UK's exit from the EU is due to talk to the first and deputy first ministers on Tuesday.
David Davis is expected to have a telephone conversation with both Arlene Foster and Martin McGuinness in the afternoon.
Prime Minister Theresa May met the Scottish First Minister Nicola Sturgeon last week.
Mrs Foster said she was looking forward to talking to Mr Davis.
"I'll be speaking to him about Northern Ireland's direct involvement in these negotiations [about leaving the EU] and I look forward to having a conversation with the prime minister face to face as well," she said.
"We are in a new era, it is time to be innovative, it is time to be open and flexible which is what the prime minister was talking about when she was with the first minister of Scotland.
"So let's think about doing things in a different way. We don't have to do things in the way we did in the past and that's what the Brexit vote is about - something, new, something different, let's think about all of that."
However, Mr McGuinness said people in Northern Ireland were alarmed about the prospect of leaving the EU.
"I'm very connected to the business community, very connected to the community and voluntary sector, very connected to the universities and I can tell you that there is absolute alarm in all of those interest groups about where we're at.
"The uncertainty, the huge challenges that they see for themselves up the road, the withdrawal of huge sums of European funding for our society - all of these things have created huge concern and disquiet and alarm.
"If Arlene's not getting that message, I'm not sure what planet she's living on."
While the UK as a whole voted to leave the European Union by 52% to 48%, 56% of people in Northern Ireland voted to remain.
Following her meeting with Ms Sturgeon on Friday, the prime minister said she was willing to listen to options" on Scotland's future relationship with the EU.
Mrs May said: "I have already said that I won't be triggering Article 50 until I think that we have a UK approach and objectives for negotiations - I think it is important that we establish that before we trigger Article 50."