Mr Lowry, of Glenreigh, Holycross who is facing four charges alleging that he filed incorrect tax returns in 2003 and 2007, has asked the High Court for permission to bring the challenge.
His trial was transferred from Tipperary to the Dublin Circuit Criminal Court after an application by the DPP, based on the amount of people who have voted for Mr Lowry in elections in Tipperary.
The trial is listed for mention on Friday in the Circuit Criminal Court.
Deputy Lowry argues that he has no outstanding tax liability and he says he is being treated unfairly and selectively when others, including certain holders of Ansbacher accounts, have not been prosecuted.
He says he wants the trial stopped on the grounds of alleged prejudicial publicity and wrongful release of information about a taxpayer into the public domain.
He says the transfer of the trial to Dublin breaches his rights and amounts to his being punished for his success as a politician in Tipperary.
He also says the trial should at least be deferred pending his appeal to a Revenue Appeals Commissioner, which is due for hearing in March, and the outcome of an investigation into his complaint over how details of a search of his home were disclosed to the media.
Mr Lowry's lawyers applied for permission to seek a judicial review.
Mr Justice Seamus Noonan directed that the other side should be present and adjourned the matter to Wednesday.
