Communities Minister Deirdre Hargey and Economy Minister Gordon Lyons, along with the Utility Regulator, met with the Chancellor in Belfast on Wednesday.
Mr Zahawi earlier told media that he would do everything in his power to deliver the money to households in Northern Ireland.
Speaking after the meeting, Ms Hargey and Mr Lyons said they are looking at the Treasury paying money to energy companies in Northern Ireland to take off customers bills.
There is to be another meeting on Monday.
Last month, the Westminster Government revealed details of the scheme in which households in Great Britain would get more than £60 off their energy bills each month throughout winter as part of its cost-of-living support measures.
The money, which is part of a package announced in May this year, will be delivered in six instalments over six months to some 29 million households.
Households will see £66 taken off their energy bills in October and November, and £67 between December and March, the Government said.
But there has been uncertainty about how Northern Ireland households will receive the payment to help with energy costs.
The region is without a functioning executive or assembly as part of the DUP’s protest against the post-Brexit Northern Ireland Protocol.
Ms Hargey said they hope to give certainty early next week.
“We are looking at a solution going forward, we have just to do a bit more work around the legalities but we have agreed that we are going to reconvene on Monday in order to sign off on a solution and give that certainty that the public rightly need,” she said.
“We’re looking at the legalities of the quickest way in order to make these payments to the energy companies so they can be taken off people’s bills directly, and that’s the bit that we’re trying to resolve as soon as possible.”
Mr Lyons added: “I have been saying for some time now that there should be a UK-wide solution to this issue, that the Treasury should pay the energy companies here in Northern Ireland in the same way as they are doing in the rest of the UK.
“I’m pleased that that view seems to have prevailed, that people now recognise that this is the easiest and most importantly the quickest way of getting this money out to people who need it during what is going to be a very difficult time.”
Earlier the Chancellor said he is also to visit Scotland and Wales, but wanted to come to Northern Ireland first to make sure the Government delivered its commitment around the energy discount.
“My pledge is that we will operationalise this and deliver it because that is what the Prime Minister wants me to do, that is what I will do,” he said.
“Today is about making sure that I work with the Utility Regulator, with the economy and community ministers to make sure we now deliver against that, and do it as quickly and as efficiently as possible, so the meeting today is to make sure we get that done.
I will do everything in my power to make sure that we deliver the money, and hence why I'm here
“I hope by the end of the meeting we’re in a place where we all know this will happen and it will happen as quickly as possible.”
Pressed on whether the energy discount would be delivered in Northern Ireland, Mr Zahawi said: “I will do everything in my power to make sure that we deliver the money, and hence why I’m here, and hence why we’re having these meetings.
“Of course I want to see the executive restored and we will do everything to try and get to a place where it is restored, that is the best place for the people of Northern Ireland, in my view.”