(CNN) Senate Intelligence Chairman Richard Burr appears to be backing away from plans to bring Trump attorney Michael Cohen in for a public hearing before his panel, breaking from the committee's top Democrat, who has called for the high-profile witness to be questioned in an open session.

Burr told CNN Wednesday that he sees little reason to bring Cohen into an open hearing after the attorney met with Senate Intelligence Committee staff for a private interview last fall.

"We've had him in for a full interview -- and I don't think we have any outstanding issues with him," the North Carolina Republican said.

Asked if there was any reason to bring him back for a public hearing, Burr said: "I don't think so."

In September, the committee abruptly postponed Cohen's closed-door interview with staff and demanded he return the following month for a public hearing, angry that he released his opening statement to the media. But a month later, the committee changed course and conducted the staff interview with Cohen. Burr and Sen. Mark Warner of Virginia, the committee's ranking Democrat, said in a joint statement that Cohen's public hearing had been postponed and would be "rescheduled at a later date."

Read More