Allan, who joined West Brom from Dundee United in January 2011, has found it difficult to break into the first team at the Hawthorns.
The 21-year-old has enjoyed spells out on loan at Portsmouth and MK Dons during the last 18 months so that he can get some first-team action under his belt.
Baggies boss Steve Clarke is thought to be keen on loaning out the Scotland Under 21 international again and a number of clubs have expressed an interest in Allan.
However, Birmingham are poised to win the race for Allan with Blues manager Lee Clark keen to add to his attacking options at St Andrew's.
Allan is thought to have agreed a season-long loan move to Birmingham as Clark tries to finalise his squad before next month's big kick-off in the Championship.