Washington (CNN) President Donald Trump's lawyers and special counsel Robert Mueller discussed a potential January 27, 2018, interview of the President before talks between the two sides stalled, sources briefed on the discussions told CNN.

The President's legal team discussed the logistics of holding the multi-hour interview session at Camp David, the presidential retreat in Maryland, the sources said. But there's disagreement among people involved over how close the two sides were to an agreement before the President's team rejected the plan.

The possible date for an interview, raised at a meeting in early to mid-January, has not been previously reported. It appears to have been the only date discussed so far, according to one of the sources.

It raises the possibility that, had they moved forward, the obstruction investigation of the President could have already concluded by now. At the time, Trump claimed to be eager to sit down with Mueller. On January 24, Trump told reporters who asked about the possible interview, "I'm looking forward to it, actually." At that same time, his attorneys were very interested in wrapping the investigation as it related to the President.

More recently, despite ongoing negotiations, the President's legal team has come to believe an interview is unlikely. That could change, members of the legal team say, and the two sides continue to trade proposals.

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