Washington (CNN) The White House may seek to prevent former White House counsel Don McGahn from complying with a subpoena issued by the House Judiciary Committee that demands his cooperation in its probe into potential obstruction of justice, CNN has learned.

A source familiar with the discussion said the White House could assert executive privilege over specific aspects if McGahn testifies, but noted that discussions are not that far along yet and added that other measures are still being considered.

Sources familiar with the matter said that the House Judiciary Committee has had discussions with McGahn's attorney, William Burck, but has not been told yet whether McGahn will comply with the subpoena, which requests documents by May 7 and his testimony by May 21. Burck did not respond to a request for comment.

House Judiciary Chairman Jerry Nadler issued a statement Tuesday standing by the committee's subpoena.

"The Committee has served a valid subpoena to Mr. McGahn. We have asked him to supply documents to the Committee by May 7 and to testify here on May 21. Our request covers the subjects described by Mr. McGahn to the Special Counsel, and described by Special Counsel Mueller to the American public in his report," Nadler said.

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