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The Blues are thought to have agreed a fee of about 10m for the 23-year-old, who is in London undergoing a medical.
"The negotiations are advancing and we expect to close a deal on Tuesday," chief executive Peter Kenyon told Portuguese radio.
Tiago is under contract with Benfica until 2007 but is keen to leave due to differences with the club's new chief Jose Veiga.
"I would not feel good if I stayed at Benfica," he told Portuguese newspaper A Bola.
"If everything goes well, my present and future will be at Chelsea."