Parkinson, who celebrates his 48th birthday this Tuesday, made the jump up into fifth place in the list following Walsall manager Dean Smith's move to Championship side Brentford on Monday evening.
The City chief has been in charge at the Coral Windows Stadium since the end of August 2011 - just over four years and three months.
Parkinson is now only below three other Football League managers in the standings - Exeter City boss Paul Tisdale (second), MK Dons' manager Karl Robinson (third), Jim Bentley of Morecambe (fourth).
Legendary Arsenal manager Arsene Wenger leads the way after holding the top job at the Gunners for a mammoth nineteen years and two months.