UPDATE on November 16 at 12:27 PM EST:
The Washington Post also reports that Craig has been chosen for the post:
President-elect Barack Obama has chosen Washington lawyer Greg Craig, who served as President Bill Clinton's lead attorney during his impeachment proceedings, to be his White House counsel, according to an individual involved with the transition.
Craig has been a longtime adviser to Bill and Sen. Hillary Clinton, but became a close adviser to Obama during the campaign, reportedly serving as the stand-in for Sen. John McCain during debate preparations.
Transition officials declined to comment. And Craig did not return calls left on his machine.
Politico reports that Barack Obama will name Gregory Craig has White House counsel:
Gregory B. Craig, a well-known Washington lawyer who quarterbacked President Bill Clinton's impeachment defense, has been chosen White House counsel by President-elect Barack Obama, according to Democratic officials.
Craig is intimately familiar with the president-elect's record because he played the role of Sen. John McCain (R-Ariz.) in debate preparations.
CNN also has a source saying Craig will be named to the post:
Prominent Washington lawyer Greg Craig will be named White House counsel for the Obama administration, a Democratic source tells CNN. The source added that it is unclear when the appointment will be made public.
Craig first gained prominence representing President Clinton in the Senate impeachment trial, but he endorsed Barack Obama over Hillary Clinton in the Democratic primaries and later played a key role in Obama's vice presidential vetting process.
Read more at HuffPost's Obama Transition BigNews Page.