Dr Haass was chosen by the Executive to lead discussions aimed at resolving the long-standing problems surrounding parades, flags and emblems and the past.
He has been meeting politicians and community leaders since the beginning of last month.
The American diplomat arrived back in NI on Monday to resume his work, he met with the leaders of the non-Executive parties and will host another round of meetings throughout the week.
These are expected to include visits to Dublin as well as talks with Secretary of State Theresa Villiers MP in London and other interested groups.
Last week Mr Haass met with Prime Minister David Cameron and this week he is expected to meet Taoiseach Enda Kenny.
"The two governments are the guarantors of the Good Friday Agreement, and if legislation was needed, the governments have got to be on board," political editor Ken Reid explained.
"It does show the significance the two governments are paying to this process."
Mr Haass said it's too early yet to be "taking the temperature" of the discussions and hopes that a point will soon come where things will "pivot".
He explained: "When you're doing a negotiation the mood changes at times, sometimes pessimistic, sometimes optimistic.
"Rarely does the change in temperature of the mood have much to do with the reality.
"I don't carry a thermometer with me to calculate the mood - it's also just way too soon to be taking the temperature, let's just give it time.
"We're still in the phase of what I would call listening and learning, there's a point at which that will start to pivot and that will happen on my next visit when we're working with the leadership of the parties to try and come to some common language."
On his last visit in September, Richard Haass had about 30 meetings with about 100 different people including politicians, academics, religious and business leaders and civil servants.
The Haass team has received around a hundred written submissions so far and most have called for progress.
Mr Haass added: "My own sense from the bulk of the submissions is that the vast majority of people are ready for compromise, are ready for progress or ready to move on."