The DPP has applied to the Court of Criminal Appeal for a hearing date in the next three weeks in the case of Anthony Lyons.
Mr Lyons, from Griffith Avenue in Dublin, is due out of prison next month after he was jailed for six months for attacking and sexually assaulting a woman on Griffith Avenue in Dublin just over two years ago.
The judge also directed the wealthy and successful businessman to pay the victim €75,000.
The Director of Public Prosecutions is appealing the leniency of the sentence.
Senior counsel Kerida Naidoo told the court that the DPP is hoping to have the case heard before Lyons is released from prison.
Mr Naidoo said submissions had been completed and would be filed by Friday. He said it should be possible to expedite the transcripts from the trial, which the defence was seeking.
Mr Justice Adrian Hardiman said he would inquire if a date could be found.
The case is due back again before the court tomorrow morning.
Lyons, who owns an aircraft leasing company, originally denied attacking the woman when arrested near the scene on 3 October 2010.
However, ten days later the 52-year-old father of four went back to the gardaí and claimed he attacked the woman because he was on cholesterol medication, a defence that was rejected by the jury.
Mr Justice Desmond Hogan sentenced him to six years in prison but suspended five-and-a-half years and ordered him to pay €75,000 to the victim.