Bush was suspended from the NBC morning show after a leaked recording of a 2005 conversation he had with Donald Trump was made public.
Carson Daly is filling in for Billy Bush for now.
An NBC source confirmed to ET on Monday that The Voice host would appear on Tuesday's Today show in place of Bush, though it is unclear whether Daly will continue to appear on the show moving forward.
Bush was suspended by NBC on Sunday after a 2005 recording was made public where the then-Access Hollywood host can be heard laughing along as Donald Trump makes disparaging comments about women, and appears to brag about being able to sexually assault people because of his celebrity status.
Bush was spotted out in Encino, California, on Monday following his suspension. An eyewitness tells ET the host looked disheveled as he wore sweatpants and flip flops.
EXCLUSIVE: Nancy O'Dell Addresses Donald Trump Comments on 'Entertainment Tonight'
Trump has repeatedly called the past comments "locker room talk," and in Sunday night's presidential debate denied ever committing sexual assault.
"Obviously I’m embarrassed and ashamed. It’s no excuse, but this happened eleven years ago," Bush told ET in a statement about the past conversation with Trump. "I was younger, less mature, and acted foolishly in playing along. I’m very sorry."
Although the Today show shakeup occurred quickly, a source close to the situation tells ET, "The staff is comfortable with how the situation is being handled."
WATCH: 'Today' Show Addresses Billy Bush's Suspension Over His 2005 Conversation With Donald Trump
Today co-host Savannah Guthrie mentioned the suspension on Monday's program, saying, "We want to note one other thing, pending further review of the matter, NBC News has suspended Billy Bush, host of Today’s third hour, for his role in that conversation with Donald Trump."
Later, co-hosts Tamron Hall and Al Roker further addressed the suspension.
"As you can see, Billy Bush is not here joining us today, as you're probably aware, part of that 2005 Access Hollywood taping with Trump that's been in the news all week," Roker said. Hall added, "NBC, which owns Access Hollywood, has suspended Billy for his role in that conversation pending further review."
WATCH: 'Today' Show Staff 'Comfortable' With Billy Bush Suspension -- But Will He Return?
Meanwhile, though some reports have circulated suggesting Bush is unpopular among his co-hosts, ET's source says, "Billy has a good relationship with each of the anchors and hosts. Let’s not forget Billy has been a part of the NBC family for a long time and they have all known him."
In any case, Bush's future at Today is uncertain.
According to Reliable Sourceshost and CNN senior media correspondent Brian Stelter, Bush "was planning to apologize on camera this time for his awful comment on that 2005 videotape."
"But on Sunday night, NBC bosses decided he would not get the opportunity to apologize at all. He would be suspended, and we don't even know for how long," Stelter told ET. "It's very possible he'll never be back on the Today show."
Watch the video below for more on Bush's Today show suspension.
