The painting was removed from display at the Royal Hibernian Academy
The artist behind nude paintings of Irish Taoiseach Brian Cowen which were hung in two public galleries could face criminal charges, according to the Press Association.
A painting of the Irish leader holding his underpants appeared in the Royal Hibernian Academy and one of him pictured on the toilet ended up in the National Gallery.
On Tuesday, the National Gallery said they had called in the police, and the painting had been up for no more than 20 minutes before it was removed.
PA has reported that the artist, Conor Casby, a 35-year-old school teacher from Dublin, voluntarily accompanied investigators to a police station to be interviewed.
It is understood he was not arrested. PA has said a file is being prepared, which could be sent to the Director of Public Prosecutions (DPP).
I would like to draw an end to this by offering the portraits to the highest bidder and donate the proceeds to charity
But another senior police source told PA it was unlikely that any charges would be brought.
Both paintings are said to have been seized by police.
Mr Casby issued a statement to the Today FM radio station in which he said would "like to draw an end to this by offering the portraits to the highest bidder and donate the proceeds to charity".
"In terms of the arguments going on in the media now, I think they're less and less to do with me," he said.
It is understood a detective called at the station's studios on Tuesday to demand details of emails between the artist and the Ray D'Arcy show.
Will Hanafin, the show's producer, said the detective told him the investigation was looking at three potential offences of indecency, incitement to hatred and criminal damage, which was hammering a nail into a gallery wall.
When he refused to hand over any information, Mr Hanafin said he was told police may now seek a search warrant.
A police spokesman would not comment on the reports, but said that their inquiries were continuing into the matter.
Irish state broadcaster RTE issued an apology at the end of its Nine News programme on Wednesday over its television report the previous evening "on the illicit hanging of caricatures of the taoiseach".