In their Championship opener, Norwich lost 2-1 to Cardiff City and they followed it up by securing a hard-fought 1-1 draw against Wigan Athletic.
Last season Birmingham City finished in a lowly 20th in the 24-team Championship. They could only manage 47 points from 46 games.
Cheltenham Town will host Birmingham City in a pre-season friendly at Whaddon Road on Tuesday.
Burton Albion will host Birmingham City in a pres-season friendly at Pirelli Park on Saturday.
With potential takeover talks making headlines in Birmingham recently, the transfer situation has reportedly taken a back seat for the club.
Winger Demarai Gray has agreed a three-year contract with Everton until the end of June 2024 with the option for a fourth year.