The Croatia international is also target for Manchester United, however Spurs would prefer to sell abroad.
Modric's former Croatia team-mate Mate Bilic was quoted recently saying he expected the midfielder to move to the Bernabeu.
"I'm very good friends with Modric," said the Sporting Gijon striker. "He wants to play in the Spanish league. He loves the Premier League but he wants to play in Spain. He's very close to agreeing a move."