The president has narrowed his list to four, according to people close to the White House — two federal appeals judges, Sonia Sotomayor of New York and Diane P. Wood of Chicago, and two members of his administration, Solicitor General Elena Kagan and Homeland Security Secretary Janet Napolitano. ... Mr. Obama talked with his legal team on Monday, and White House aides said an announcement could come as early as Tuesday. - NY Times
Note that the source of the list of names comes from outside the White House, but the timing comes from inside the White House.