Parkinson has been shortlisted for the League 1 Manager of the Month award, while Burke has been put in the running for the Player of the Month award.
Parkinson is up against Gary Caldwell of Wigan Athletic, Chesterfield's Dean Saunders and Scunthorpe United manager Mark Robins for the managerial gong.
Along with Burke, Coventry City striker Adam Armstrong, Millwall attacker Aiden O'Brien and Peterborough United's Jon Taylor have also been shortlisted for the player award.
After guiding City to three wins and two draws from the club's five games throughout the month, Parkinson managed to keep the Bantams unbeaten during October.
Parkinson's men defeated Rochdale, Doncaster Rovers and Bury, whilst they also picked up praiseworthy draws against Wigan Athletic and Millwall.
With Burke continuing to look wise beyond his years at the back alongside Rory McArdle, the loanee West Ham defender helped City to two clean sheets during October.
In total, Parkinson's side actually only conceding three goals in their five league matches during the month.
Both the Manager of the Month and Player of the Month award winners for League 1 will be confirmed on Friday (6 November 2015).