The league has submitted follow-up questions to Elliott about the claims made in July, sources told ESPN's Adam Schefter.
Elliott, 21, is still in the process of responding to the questions, which he received within the past month, according to Sunday's ESPN report. Any potential discipline from the NFL would be for the 2017 season.
Elliott, the league's leading rusher as a rookie, was accused of a second domestic violence incident involving the woman, who said she was hurt in a July argument.
Police in Aventura, Fla., were also called to Elliott's apartment in February -- months before the 2016 NFL Draft -- to investigate an altercation involving the same woman, according USA Today.
Over the summer, Elliott's ex-girlfriend posted pictures of her bruised arms on Instagram and tagged Elliott, sparking an investigation that has lasted the entire season.
Elliott, who was not arrested and did not face charges related to the alleged incidents, said he was interviewed by the NFL during the season. He insists he did nothing wrong.
The league's investigation will determine whether Elliott violated its personal conduct policy.
NFL commissioner Roger Goodell said last month there is no timetable for concluding the investigation.
"Well, the best way to be fair to a player is to be thorough and to take your time and get it right," Goodell said of the investigation that began in July. "So, that is what we're working on. We have professionals that are working on this. We're not putting a timetable on it. We want to make sure they get it right, they get all the facts. And when they reach a conclusion, we'll all know about it."
Elliott, drafted fourth overall by the Cowboys out of Ohio State, finished as the NFL's leading rusher with 1,631 yards on 322 carries. He also ran for 15 touchdowns, and caught 32 passes for 363 yards and a score.
The Cowboys host the Green Bay Packers on Sunday in an NFC divisional playoff game.