Haass and Harvard Professor Meghan O'Sullivan were brought to Northern Ireland in July to resolve a number of contentious issues, including the display of national flags, the holding of parades and how to deal with a history of violence.
Talks were held for eight hours in Stormont, Ireland, and ended early Tuesday, the BBC reported.
"Let me be clear about this, we don't have an agreement. [But] in no way have we given up on the possibility of still reaching agreement before the end of the year," he said, citing the Dec. 31 deadline.
Haass, who is returning home for Christmas, said he will send the negotiators a fifth set of proposals.
"Yes, it's true that the work done on flags is quite disappointing by any measure but the other two areas, are I believe, quite impressive. I believe it would be a real shame not to turn that work into a reality."