Rousseff, accused of taking unauthorised loans to patch up the state budget during her 2014 reelection campaign and in early 2015, was suspended for the trial on May 12.
The suspension can run as long as six months, but acting president Michel Temer's team argued for ending far earlier, possibly even before the start of the Rio Olympics on August 5.
"For us, for the Temer government, it would be best if it were as quick as possible, while respecting the rules laid down by the Supreme Court," Temer's chief of staff Eliseu Padilha said.
Rousseff's lawyer, Jose Eduardo Cardozo, called the impeachment process "a huge farce" and a "coup."
The Senate will try Rousseff and must vote by a two thirds majority to remove her from office.
Temer, who was her vice president, would then stay until scheduled elections in 2018. Anything less and Rousseff would return to power.
The impeachment trial comes on top of a huge corruption scandal centred on state oil company Petrobras.
Two of Temer's ministers implicated in the scheme have been forced to resign in the last few days after secret recordings of them apparently criticising the probe were released to the media. In one of them, planning minister Romero Juca appeared to be saying that the impeachment could be used to block investigators.
Rousseff, who is blamed by many Brazilians for a deep recession and the political crisis, has rock bottom popularity ratings -- as does Temer.
In the midst of the turmoil, Brazilian deputies approved a big salary increase for civil servants and the military yesterday.