Marshall Grossman, the Los Angeles litigator hired by Bush last week, tells ET, "We are continuing with negotiations and hope to have a resolution today or tomorrow."
This comes after Grossman released a statement on Friday, denying reports that a $10 million settlement had been reached.
"That report is false," Grossman told ET late Friday. "There is no $10 million agreement and that amount has not been discussed. Negotiations are ongoing between the parties."
Bush's suspension was handed down in response to his role in the 2005 tape of Donald Trump making lewd comments about women, in which the then-Access Hollywood host could be heard laughing along.
Harry Connick Jr. filled in for Bush during the 9 a.m. hour of Today on Monday and is set to return on Tuesday. The entertainer was a big hit, charming the co-hosts with his dance moves.
"I was so excited when I heard I was invited to the show, because I'm a big fan of the show!" Connick Jr. gushed on air.
For Bush's part, he has apologized for the Trump tape, telling ET in a statement shortly after it surfaced, "Obviously I'm embarrassed and ashamed. It's no excuse, but this happened 11 years ago -- I was younger, less mature, and acted foolishly in playing along. I'm very sorry."
Grossman defended Bush's role in the tape.
"If Billy had been passive or responded 'Shut the f**k up' to Trump, Billy would have been out of a job the next day," he told ET.