Ranieri is ready to offer Spurs boss Harry Redknapp a cash-plus-player deal in a bid to sign Modric in January.
It is believed Ranieri is ready to offer Vincenzo Iaquinta as part-exchange.
Modric has admitted in the press lately that he wants to stay at White Hart Lane.
The 23-year-old said: “Of course, in football you never know what might happen but my plan is to stay here because I am very happy.
“It’s been a bad start but with Harry coming in we are improving. I believe we have an extremely good team and that this club should be at the top.”