But Gianluca Savoini, whose voice was identified on a covert recording of the talks in Moscow, invoked his right to remain silence, according to the reports.
The first stories of the October meeting at a Moscow hotel appeared in the Italian press in February.
But the publication last week by online news website Buzzfeed of a transcript of the talks — taken from an audio recording — pushed it back centre stage and was widely reported in Italy.
The deal under discussion was to covertly divert $65 million (58 million euros) to the League by means of discounted Russian oil transactions through intermediaries.
Buzzfeed said it was not clear whether the proposed deal ever came to fruit.
Former journalist Savoini, 56, is married to a Russian and is president of the Lombardy-Russia association. He is considered one of the League's main contacts with Russia.
Salvini has denied taking money from Russia, but has been called on by opposition parties to answer to parliament.
Asked by reporters Monday whether Salvini should do so, Italy's Prime Minister Giuseppe Conte said “why not?”
“We believe in transparency in every seat of office, parliament first of all.
“Our guidelines are clear: absolute transparency for Italian citizens and absolutely loyalty to national interests. And on this, the government will not budge an inch,” he added.
One of the other two Italians present with Savoini at the Moscow meeting, lawyer Gianluca Meranda, may be questioned by prosecutors in the coming days, media reports said.
Salvini has never hidden his admiration for Russian President Vladimir Putin, who visited Italy at the start of the month.
And during his visit, Putin referred to a cooperation agreement between his United Russia party and Salvini's League.
But Salvini's says his support for Putin, his fight to overturn European sanctions imposed against Russia for their 2014 annexation of Crimea from Ukraine, comes “free”.