Senegal left-back Drame is currently on trial at St Andrew's and is keen to impress Blues boss Alex McLeish.
Drame is contracted to Ligue 1 side Sochaux but feels his future lies elsewhere.
He said: "I was on loan last season at Real Sociedad. I am here now to show Birmingham I want to join them.
"The Premier League is for me the best league. I am settling well here and I want to play in this team.
"The coach at Sochaux [Francis Gillot] does not want me, but that is football.
"Hopefully I will earn a contract at Birmingham."