The statement marks a shift in the stance of the French media group as TIM's investors get ready to evaluate a 10.8 billion euro ($12.2 billion) takeover plan presented by U.S. fund KKR for TIM.
Until now the French group has dragged its feet on the possibility that Rome gains control over TIM's fixed network.
A spokesperson for the French media group told Reuters that Vivendi was interested in any solution that "promoted the efficiency and modernity of the network, while preserving the value of its investment".
"In this perspective, the hypothesis of a state control of the network, if it could lead to an institutionally guided strategic project, will certainly be evaluated with openness," the spokesperson added.
TIM's fixed line business provides Italy's main telecoms infrastructure and plays a major role in broadband rollout efforts on which Rome plans to spend billions of euros of European Union funds to improve coverage.
State investor CDP has taken a 10% stake in TIM to oversee the network and is expected to play a key role in any plans to carve out the grid.
($1 = 0.8839 euros)
(Reporting by Elvira Pollina and Francesca Landini; writing by Francesca Landini; editing by David Evans)