Changing the date of the Democratic convention would be a logistical feat, requiring a rebooking of thousands of hotel rooms along with the arena and conference center space in Milwaukee — or another city if the event is moved.

Before Mr. Biden’s call to change the convention’s date, Democrats planning the party’s quadrennial gathering had been in touch with officials from Fiserv Forum, the host arena, about alternate dates.

The two most likely new slots are Aug. 17 to 20 and Aug. 31 to Sept. 3. The arena is available those weeks, according to a Milwaukee Bucks official.

The Republican National Convention is scheduled for Aug. 24 to 27.

Milwaukee’s arena and convention center space is booked Aug. 10 to 12 by the insurer Northwestern Mutual’s annual meeting, which draws more than 12,000 people to the city, according to The Milwaukee Journal Sentinel.

Joe Solmonese, the chief executive of the Democratic National Convention, said in an interview Monday that he had six to eight weeks before any decisions must be made about moving the convention. Mr. Biden’s announcement is likely to hasten such choices.

“Providing an opportunity for our candidate to reaffirm our democratic values, unify the party and share his vision for a safer and stronger future for our country has never before felt more important,” Mr. Solmonese said Wednesday before Mr. Biden called for moving the convention. “As we continue to put plans in place for a successful Democratic National Convention this summer, we will balance protecting the health and well-being of convention attendees and our host city with our responsibility to deliver this historic and critical occasion.”

If the convention were moved, it would also affect how much money the party’s nominee would be able to spend over the summer. Candidates have separate pots of money they can tap into in a primary and a general election. The longer Mr. Biden is not the official nominee of the party, the less time he has to spend general election funds his campaign has raised.