If her opponents garner a simple majority of the 81 senators, Rousseff will be suspended for up to six months during the trial and Vice President Michel Temer will take power.
With well over half of senators telling newspapers they will vote to try Rousseff, Brazil's first female leader is expected to leave the Planalto presidential palace on Thursday, following 13 years of leftist Workers Party rule in Latin America's largest economy.
The political crisis has hit at a time when
Senators are due to start discussion of the motion at 9 am (1200 GMT) after each member of the upper house gets the chance to speak. The final vote is expected to take place around 8 pm (2300 GMT).
Rousseff, who has said her impeachment is illegal and branded it a 'coup,' has vowed to fight the process until the last minute. Her government appealed to the Supreme Court on Tuesday.
"I will not resign, that never crossed my mind," Rousseff said in a speech on Tuesday, to cheers from supporters.
The economic crisis and the Petrobras investigation have paralyzed Rousseff's second-term administration. There are worries the tense political situation may spark protests that could turn violent.
On Wednesday, anti-impeachment protesters blocked roads with burning tires around
The vote will cap a chaotic week that started with the newly installed speaker of the lower house, Eduardo Maranhao, saying he had annulled the full chamber's April 17 vote to impeach Rousseff. He argued the vote contained procedural flaws.
Senate leader Renan Calheiros promptly rejected his decision and said the upper house would press forward with impeachment proceedings.
Maranhao withdrew his decision on Tuesday, following complaints it was illegal. That cleared the way for the Senate vote.
If the case goes to a trial in the Senate, presided over by the head of the Supreme Court, Rousseff's opponents are confident they can muster the two-thirds of the 81 senators, or 54, needed to unseat the unpopular president. Temer would then fulfill the remainder of her mandate until elections in 2018.