The IAFF is one of the most influential labor groups in the U.S. Biden is especially close to labor, which could be a key constituency for him if he seeks the White House.
Schaitberger declined to comment on the call, saying he does not discuss private conversations. But the source said Biden talked about campaign strategy with Schaitberger and indicated a final decision on whether he would run for president is imminent.
The source described the call as one of many the vice president is making to potential backers of a Biden candidacy.
Earlier this month, the New York Times reported
the IAFF informed Hillary Clinton's campaign that it had abandoned its plans to endorse the former secretary of state. And in a profile on Friday, the Times reported
Schaitberger's "close, longstanding relationship" to Biden, saying he personally lobbied the vice president in 2009 to expand a law that helped avert firefighter layoffs during the Great Recession.
This past week, Schaitberger suggested to New York Magazine
that if Biden ran, he'd get the union's backing.
"If the VP were to announce his candidacy, our membership would certainly be very inclined to support that candidacy," he told the magazine.
On Thursday, CNN reported that Biden has personally made a series of calls this week to Democratic strategists from Iowa, New Hampshire and South Carolina, asking a final round of detailed questions about how -- not whether -- to launch a 2016 presidential campaign.
People familiar with the conversations tell CNN that Biden has been making the calls throughout the week
, including on Wednesday, just as many leading Democrats argued the window to a potential candidacy was closing in the wake of Clinton's strong performance in the party's first presidential debate. He is asking these people to work for him if he runs.
Former Delaware Sen. Ted Kaufman, a member of Biden's close inner circle, sent an email late Thursday to a network of Biden alumni, obtained by CNN, saying that while he doesn't know when Biden will decide, he knows Biden is aware of the ticking clock.
"On the second question - timing - I can't add much, except I am confident that the vice president is aware of the practical demands of making a final decision soon," Kaufman wrote. "He has been in public and political life a long time and he has a good grip on the mechanics around this decision."
Asked about a potential Biden run at a White House press conference on Friday
, President Barack Obama declined to comment, instead praising the Democratic field at large.
"I'm not going to comment on what Joe's doing or not doing. I think you can direct those questions to my very able vice president," Obama said.
The same day, in an interview with CNN's Jake Tapper
, Clinton said she believes Biden is entitled to his own timeline in making his decision.
"That's up to Vice President Biden," she said. "Certainly I'm not in any way suggesting or recommending that the vice president accept any timetable other than the one that is clicking inside of him. He has to make this decision."