A few of the fundraisers have gone public with their presidential preference. Others have quietly decamped and signaled their intentions to the Draft Biden 2016 super PAC that is working to prod the vice president into the race for the White House.

“Instead of being ready for Hillary, we’re waiting for Joe,” said Bill Bartmann, the founder and chief executive of CFS2 Inc., and onetime donor to Mrs. Clinton’s friendly super PAC. Mr. Bartmann’s switch in allegiance prompted one Clinton campaign official to contact him and ask: “Why are you doing this?” he said.

Clinton fundraisers say they don’t expect many supporters to switch teams, should Mr. Biden enter the presidential primary race. Her campaign didn’t respond to a request for comment.