A deal has been agreed between the two clubs and Spillane is now in the process of finalising personal terms, with an agreement expected to be completed before the weekend.
Spillane has been an integral part of Dagenham's side this season, making 27 starts and scoring five goals, although he has not made an appearance since the 3-1 defeat at Northampton on New Year's Day.
Daggers boss John Still is understood to be keen on an unnamed youngster at Birmingham as his replacement.
Meanwhile, Dagenham have extended Jake Caprice's loan stay from Blackpool until February 9.
The midfielder initially joined the Daggers on a month-long deal in November but has earned a prolonged stay at Victoria Road, making six substitute appearances in total.
Still said: "Jake has done well since being with us and we like him. He has made some substitute appearances, in which he has played well in, and he will now spend his third month with us."