"The time has come for Muzzy to move to club where he can better himself," Barnet said.
"Muzzy has given sterling service to Leicester for a number of years.
"There been no shortage of interest in him, but nothing will be finalised until the summer."
As well as Birmingham, Celtic, Aston Villa and Blackburn Rovers are also reportedly interested in Izzet, who will be available on a free contract at the end of the season.