Renzi will meet Putin on Thursday morning for discussions that will also include developments in Ukraine following a ceasefire last month, La Stampa reported.
The premier will also lay flowers in the area near the Kremlin where Russian opposition politician Boris Nemstov was shot dead on Friday, the newspaper said.
Nemstov, a staunch critic of Putin, was due to lead an opposition rally on Sunday.
Despite blame being pointed towards the Russian government, the murder isn’t expected to disrupt the meeting’s agenda, La Stampa said.
Renzi last week appealed for international help over the situation in Libya amid threats from Isis extremists, who have threatened to use the north African country as a springboard for attacks in Europe.
Although Italy has been pushing its allies to take a more proactive approach to the situation, Renzi has ruled out intervention in the short-term.
“The important thing is to get the message across that the UN must play a role in the Libya situation, and Russia is a permanent member [of the UN Security Council]," he said last week.
Italy had long enjoyed good relations with Russia, mostly cemented when Silvio Berlusconi was leader, until the Russian-Ukraine conflict and is considered by some as only a moderate supporter of the sanctions against Russia.
This will be Renzi's first visit to the Kremlin since becoming premier in February last year. The pair last met in Milan in October, at a summit of European and Asian leaders (Asem).