Blackpool are looking for their third manager this season after Michael Appleton left the club on Friday to join Championship rivals Blackburn Rovers on a two-and-a-half year contract.
Appleton had only been in charge at Bloomfield Road since early November after he left Portsmouth to replace Ian Holloway, who was appointed Crystal Palace boss.
Bradford manager Parkinson had emerged as an early contender to succeed Appleton, but Sky Sports sources understand he does not want to discuss the position.
Parkinson has led Bradford to the brink of the Capital One Cup final after the League Two club enjoyed a stunning run through the competition.
After knocking out Wigan Athletic and Arsenal on penalties in previous rounds, the Bantams beat Aston Villa 3-1 at home in the first leg of the semi-final on Tuesday night.
And it appears that Parkinson has no plans to walk away from Valley Parade, with Bradford also pushing for promotion to League One this season in addition to a trip to Wembley.