Parkinson has been shortlisted for the award alongside Scunthorpe United's Graham Alexander, Wigan Athletic boss Gary Caldwell and Oldham Athletic manager John Sheridan.
Parkinson's nomination comes after he guided City to four wins and a draw in the month of April. The Bantams' only defeat during this period came via a 1-0 loss at Coventry City.
In a month which saw City confirm their spot in the end-of-season Play-Offs, the Bantams' most notable victory throughout April was arguably their 4-0 home success over fellow promotion-contenders Walsall.
The winner of the award will be confirmed this Friday (6 May 2016).