With a series primary votes on Tuesday that could see Clinton all but seal the party nomination, the White House refused to rule out an endorsement within days.
"Once the voters in New Jersey and California have an opportunity to express their preference," said White House spokesman Josh Earnest, "then we may be in a position where we have a much greater sense of what the outcome is likely to be."
It is an open secret in Washington that President Barack Obama intends to endorse Clinton. But the White House has publicly been wary of putting Obama's hand on the scale during a surprisingly long and sometimes bitter primary race against leftist Bernie Sanders.
White House officials have been wary about alienating millions of young voters who have flocked to Sanders' strident campaign, which has given voice to popular anger about income inequality.
"I think the Sanders campaign would agree that the president has worked hard and gone to great lengths to be fair," said Earnest.
But he added: "The president does have a long personal relationship with Secretary Clinton, she served as his secretary of state for more than four years." Sanders -- a 74-year-old senator from Vermont who was an independent until recently -- has won 10 million votes during the primaries, three million fewer than Clinton.