The 25-year-old striker started training with Blues on Monday after passing a medical, but is unable to make his debut until the club receive a permit for the Trinidad & Tobago international.
Blues boss Steve Bruce is hopeful John will receive international clearance in time to play in the away game at Bradford on Sunday.
"We hope it comes through by the end of the week and we are doing all we can" Bruce told reporters.
"I have no doubts at all that Stern will be a big asset for us."
John, who has scored 14 goals for Forest this season, added: "Hopefully I can score some goals for Birmingham to help us get into the Premiership."