The rehearsal is now planned for Monday, according to the report.
Biden's team had also canceled an Amtrak trip from Wilmington to Washington planned for Monday due to heightened security concerns, the report added. Biden will be inaugurated on Jan. 20.
The presidential inaugural committee declined to comment on the report.
Federal Bureau of Investigation Director Christopher Wray said earlier that the FBI was looking into individuals who could possibly threaten the safety of the inauguration.
A presidential inauguration traditionally draws hundreds of thousands of visitors to Washington, but the ceremonies have been scaled back dramatically because of the COVID-19 pandemic.
Biden asked his nominee for deputy attorney general and former President Barack Obama's counter-terrorism adviser, Lisa Monaco, to serve as a temporary homeland security adviser leading up to next week's inauguration.
Officials have warned of plans for armed protests in Washington and all 50 states and activist groups have been concerned about the potential for violence.
The warnings follow last week's assault on the U.S. Capitol by supporters of President Donald Trump that left five people dead.
Trump's supporters stormed the Capitol last Wednesday, trying to halt the certification by Congress of Biden's election win.
Trump, who has challenged the validity of Biden's victory without producing evidence, initially praised his supporters but later condemned the violence.