The purchases amount to a 0.86 percent stake in Telecom Italia, according to Reuters calculations.
Vivendi had a 20.5 percent stake in Telecom Italia at a Dec. 15 shareholder meeting of the Italian company.
At that meeting the French group won a vote to appoint four representatives to Telecom Italia's board while also blocking a share conversion plan that would have diluted its stake.
If no shares have been sold in the meantime, the new purchases would take Vivendi's stake to around 21.4 percent.