Mr Biden’s former Chief of Staff, Moises “Moe” Vela, explained “it’s tradition” for the sitting president to hand power over to the President-elect.
He admitted he thinks it’s unlikely Mr Trump will make an appearance given how hard he has contested the US election results.
“I will go out on a limb on your show… I don’t think that he will show up,” he told Today.
“That is my prediction. It is sad and disappointing to see somebody behave that way as an adult. We come to expect that from him, as you know. It’s OK.
“Is he welcome? Of course he is welcome.”
Mr Vela’s comments come after Mr Trump took to Twitter to confirm the formal transition of the US government to Mr Biden’s incoming administration on Monday.
Mr Vela said if Mr Trump doesn’t show up it will not overshadow the event, which will in part celebrate the diverse cabinet Mr Biden has began to assemble.
“You know what, that’s not his day,” he said.
“That is Joe Biden’s day. That is Kamala Harris’s day. That is a day that we get to celebrate this incredible diverse staff and Cabinet and women included.
“It will be amazing and so beautiful to watch this develop.
“I can’t wait. I hope that I am on (Today) with you on the 21st and I want you to look in the camera and say president Joe Biden.”