However, "until someone has those numbers, the race goes on," Clinton campaign manager Terry McAuliffe told CNN.
The final primaries were Tuesday in Montana and South Dakota.
McAuliffe said during NBC's "Today" show he thinks if the Illinois senator reaches the 2,118 delegate threshold, the former first lady "will congratulate him and call him the nominee," The Hill reported.
"I can unequivocally say, though until someone has the numbers, the nomination fight should continue," McAuliffe told CNN. "Right now ... nobody does."
He said reports about Clinton conceding Tuesday night were "100 percent incorrect."
"Senator Clinton will not concede the nomination (Tuesday) evening," an official statement from the Clinton campaign said.
McAuliffe said Clinton, who will watch the returns from her home state of New York, will talk about the 18 million people who have supported her and "all the issues that matter to her."
He said Clinton expected to talk to superdelegates to press her case about being the better candidate to face presumptive Republican nominee Sen. John McCain in the general election.