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The Royals skipper has been unable to get into the team this season and has recently had his first team opportunities limited further as the Royals swooped to sign Steven Sidwell.
The U's are seeking a new boss after dismissing Steve Whitton from his role two weeks ago and are believed to want to appoint a managerial newcomer.
Colchester are believed to have had over 50 applications for the vacant post. Parky is the favourite for the post but former Darlington boss Tommy Taylor, Burton boss Nigel Clough and former boss Steve Wignall are also believed to be in the frame.
Parkinson is out of contract in the summer but has been offered a coaching role with the Royals for next summer. However, the veteran midfielder is believed to be interested in taking over the reigns at Layer Road, making his first step onto the managerial ladder.
"There has been interest from Colchester about me becoming manager and I am flattered by that, but I'm very happy at Reading," admitted Parkinson, speaking to the Reading Evening Post.
"The manager and chairman have spoken about giving me a coaching contract, but you never say never in life.
"I have had a brief chat with Colchester's chairman, nothing major, and he has a lot of options with a lot of people applying for the job. But it is nice to be thought of and nice to know someone has done their homework on you."
Parkinson, who has already completed his UEFA A coaching badge, will take control over Reading's reserve team tonight when they take on Portsmouth.