"Our union is preparing as if the vice president is going to announce his candidacy," Schaitberger told CNN Tuesday. His union would not undergo such an effort, he added, "unless (they thought) there was a candidacy."
Schaitberger described Biden as "thoughtfully and deliberately" working his way through the decision-making process, but the firefighter union president declined to put a timeline on the vice president's final determination, based on their conversations.
Biden is looking at the "financing ... infrastructure" needed to mount a campaign, Schaitberger added.
The union president sought to quell expectations for a speedy decision from Biden, calling timelines described in recent news reports "not really accurate."
The International Association of Fire Fighters 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.
Earlier this month, The New York Times reported
the fire fighters union 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
on 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.
Getting ready for a run
Biden's associates are setting up interviews for potential staff positions on a Biden presidential campaign, a source familiar with the process told CNN.
Biden met with his top political advisers Monday night -- the same group he met with at least twice last week.
Also last week, Biden made calls throughout the week to ask Democratic operatives and officials to work for him if he does enter the 2016 race, people familiar with the conversations told CNN.
Biden spoke Monday at a White House summit on climate change -- but he offered no clues about his pending decision.
He opened the session, to which he was 10 minutes behind schedule, by calling himself "the late Joe Biden" and saying he'd spent the last two hours meeting with President Barack Obama "on other matters" -- which he didn't further explain. Treasury Secretary Jack Lew was also scheduled to be in that meeting.
Pennsylvania Democratic Rep. Brendan Boyle, who tweeted Monday morning that he has a source who says Biden will run for president, said he is confident his information is accurate and that an announcement is coming "very soon."
"If he didn't run, it would be pulling back from a decision that's already been made," Boyle told CNN. The congressman declined to reveal his source but described it as "very close to the Biden camp."
Polling hasn't shown a groundswell of support for Biden. A CNN/ORC national poll out Monday
shows that just 18% of Democratic primary voters would back Biden, behind Clinton at 45%, and Vermont Sen. Bernie Sanders at 29%.