Inter president Erick Thohir has confirmed Sagna is on the San Siro club's radar as they begin early preparations for next season.
"We're interested in Sagna because we need to balance the team," Thohir was quoted as saying on the club's official website.
"Right now we only have (Yuto) Nagatomo and Jonathan. If one of them gets injured you need somebody else to come in."
Sagna could still sign a new deal to remain in north London, while he has also been linked with a move to Manchester City.
"If Sagna decided to stay in England, we'd understand and in that case we might bring in a young player from our academy," Thohir added.
The Inter owner ruled out a move for veteran Manchester United defender Patrice Evra, adding: "We've never had any negotiations with Evra".
Inter have already begun preparations for next season following a disappointing campaign.
Walter Mazzarri's side are 31 points adrift of champions-in-waiting Juventus and face a fight just to qualify for the Champions League.
Thohir has previously suggested that a high-profile striker would also be high on the list of priorities, with Chelsea forward Fernando Torres and Manchester City's Edin Dzeko both linked, amongst a host of names.
Thohir did not rule out a move for either, but will talk with his coach before any decision is made.
He added: "What I said is that we need someone up top. The media have written about those players and I mentioned that one of them would be good for Inter.
"It depends on the discussions we have with the coach and the management about how we can be more consistent up front. In the end it depends on the players, the formation and the strategy that we want to use."
Asked if he was happy with Mazzarri, Thohir added: "I don't have any problem with him or with the management.
"When it comes to the end of the season we review everything, for example if our website's not doing well, why that is, how do we improve ticketing and so on. As a businessman I need to review things."