The Biden campaign declined to comment.
Mr. Biden told donors in late April that Mr. Kaufman was helping steer the early formation of a transition team. “You can’t wait until you win, if you win,” Mr. Biden said. “You’ve got to start right now.”
Mr. Kaufman worked on transition-planning legislation during his time in the Senate. Under the current law, the nominees of major parties gain access to federal money for office space, computers and other services beginning in September, but must raise funds to pay for personnel.
The Center for Presidential Transition, an arm of the nonprofit group the Partnership for Public Service, estimates that total costs run $10 million to $12 million, with the federal government paying about half, including staff salaries after the election for the president-elect.
The Biden transition committee has raised nearly $700,000, according to a person familiar with the matter.
“What the Biden team is doing is totally in line with what prior candidates have done and what best practices are in terms for transition planning,” said David Marchick, the director of the Center for Presidential Transition.
Mr. Biden has expressed some skepticism that the Trump administration will make a potential transition easy.
“The Bush administration worked very closely with Barack and me, with our administration, in terms of handing over power in the transition,” Mr. Biden said in April, recalling the process in 2008. “I hope it’s as smooth as it was then. I doubt it, but I hope so.”
Other officials the Biden campaign has announced hiring for the transition are Avril Haines, a deputy national security adviser during the Obama administration who will manage national security and foreign policy planning; Angela Ramirez, the chief of staff to Representative Ben Ray Luján, Democrat of New Mexico; Gautam Raghavan, the chief of staff to Representative Pramila Jayapal, Democrat of Washington and a co-chair of the House Progressive Caucus; Julie Siegel, a former top adviser to Senator Elizabeth Warren; and Ms. Ryan, the former Biden aide, who is married to Antony Blinken, a top Biden foreign policy adviser.