This page contains all the information you need on how to have a romance with Thane Krios.
Huerta Memorial Hospital
Once you’ve completed the necessary steps to continuing the romance with Garrus which can be found here, How To Start Thane Romance. Now you’ll want to speak with Commander Bailey after the mission, Priority: Citadel II,, then speak with Thane to say your final goodbyes, as unfortunately his disease has reached its final stages. As you continue progressing through the game, be sure to regularly check your Private Terminal for one final message from Thane.
Your romance will conclude properly in the Citadel DLC, as you’ll hold a funeral for him. After the funeral, go up to the bedroom on the top floor of the apartment and watch the video from Thane.