Modric himself has broken his silence on the matter, and says he wants to end his spell at White Hart Lane.
Speaking to the Daily Mail, he said: "I want to leave Tottenham as friends. I have enjoyed my time there, but now it is right for me to look at another club.
"I have an arrangement with the chairman. When I signed my new contract, he said that, if another club came to sign me, they would consider the offer."
Modric has also been strongly linked with Manchester United in recent weeks, but it appears he's set his heart on a move across the capital to Stamford Bridge.
He added: "Chelsea are a big club with an ambitious owner. They have great players and they have ambitions to fight for the title and win the Champions League.
"I want to stay in London. I am very happy here and so are my family. I like the city."