The GUE/NGL group in the European Parliament, which Ms Salis will join if she takes up her seat, said it had been in contact with her father after her election.
Her defence team said her election to the EU Parliament meant she could ask for immunity.
“We have had six MEPs elected, and among these is Ilaria Salis,” Nicola Fratoianni, one of the party’s leaders, said on Monday.
“Now we want Ilaria here in Italy – free, and with immunity, ready to carry out her mandate,” he said.
Ms Salis’s legal team can request immunity before July 16.
“With the election, she acquires parliamentary immunity under the EU Treaty” that provides for the “exemption from any form of detention and suspension of criminal proceedings” for parliamentarians, her lawyer, Eugenio Losco, told AFP.
“Ilaria Salis has a right to this immunity,” which the legal team will request once she is officially proclaimed an MEP, he said.
Her trial began last month.
Elsewhere, an ethnic Greek Albanian was elected as a MEP in Greece despite being in jail in EU candidate country Albania, where immunity does not yet apply.
In March, Fredi Beleri, was sentenced to two years in prison for buying votes ahead of his election as mayor of the Albanian town Himara in May 2023.