Lille reportedly turned down an initial €5m offer from Inter for their French international right-back Mathieu Debuchy.
The Nerazzurri have long shown an interest in Debuchy, who is currently on international duty at Euro 2012.
The Italian media claim Inter made an opening bid of €5m which was rejected by Lille.
Debuchy’s price-tag is closer to €9m, but Inter are apparently unwilling to go beyond €7m.
Newcastle United and Chelsea are also tracking the player, which increases the pressure on Inter to enter a bidding war.
He turns 27 next month and can also play in a more advanced wide role.
Think you know your Italian football? Share your knowledge, tips and comments to win cash prizes in OLBG's tipster competition - £5,000 monthly.