The 21-year-old forward is a free agent following his release by Sheffield United in January and has been on trial with the Sky Blues recently.
City boss Mark Robins, who has again dismissed speculation linking himself with various managerial vacancies in the Championship, said: "Danny has been with Sheffield United for a couple of years and prior to that had been acquired by Chelsea.
"This fits into our policy of trying to develop younger players who can step through to the first team. We will assess the situation at the end of the season, while giving Danny the opportunity to earn himself a longer-term contract."
