The idea is to widen the global discussion on the crisis to countries including Russia and China.
China, a G20 member, may be set to play a bigger role in Afghanistan after the Taliban swept to power last month and Western forces withdrew.
For Beijing, a stable and cooperative administration in Kabul would pave the way for an expansion of its overseas infrastructure drive, analysts say.
The Taliban, meanwhile, may consider China a crucial source of investment and economic support.
On Friday, a Taliban spokesman said Beijing had promised to increase humanitarian aid to the war-ravaged country.
Italy's foreign minister Luigi Di Maio said Tuesday that the ministry was working to "verify the conditions, modalities and timetable" for holding such a summit.