The Bradford City boss is out of contract at the end of the season and it is understood that the Royals are keen to speak to him.
However, Parkinson - who made over 350 appearances for Reading - is taking no notice of the speculation and is currently in talks with Bradford over a new contract.
"Obviously I played there a lot of years and I've been linked with that job when it's come up previously," said Parkinson, who was also assistant manager at the Madejski Stadium when Alan Pardew was in charge.
"It happens and you take no notice of it and carry on with the job."
Parkinson made history this season when he led Bradford to the Capital One Cup final, beating Premier League sides Wigan, Arsenal and Aston Villa along the way.
The 45-year-old attracted from Championship sides Blackpool and Blackburn Rovers, but opted to stay at Valley Parade as the Bantams became the first team from the fourth tier to reach a major final since 1962.
Reading academy manager Eamonn Dolan will take charge for Saturday's game at Manchester United and the club hope to have a replacement in place for the trip to Arsenal on 30 March.
Former Southampton boss Nigel Adkins, Gus Poyet and Roberto Di Matteo have all been linked with the post.