The board of the Museion museum in the city of Bolzano was meeting today to decide whether to comply with the wishes of the Pope and other opponents of the 1.3m (4ft) wooden sculpture, Reuters reported.
The work by the late German artist Martin Kippenberger is called Zuerst die Füsse (Feet First). The frog with its tongue hanging out is wearing a green loin cloth and is nailed through the hands and feet on a brown cross in the manner of Jesus Christ.
Museum officials in the Alto Adige region near the Austrian border said Kippenberger, who died in 1997, considered it a self-portrait illustrating human angst.
But Franz Pahl, the president of the regional government, was so enraged by the sculpture he went on hunger strike to demand its removal and consequently ended up in hospital during the summer.
"Surely this is not a work of art but a blasphemy and a disgusting piece of trash that upsets many people," he told Reuters before the start of the board meeting.
In a letter of support for Pahl, the Vatican said the sculpture "wounds the religious sentiments of so many people who see in the cross the symbol of God's love".
However, Claudio Strinati, a superintendent for Rome's state museums, told an Italian newspaper today that censoring the work would be wrong.
"Art must always be free and the artist should not have any restrictions on freedom of expression," he said.
Kippenberger's work has been shown at Tate Modern and the Saatchi Gallery in London, and the Venice Biennale. Retrospectives are planned in Los Angeles and New York.