Colchester have refused to terminate his contract as it still has a year remaining on it, and will address the issue when the 38-year-old returns from holiday in a week's time.
City chairman Adam Pearson is monitoring the situation: "If Phil Parkinson has resigned then that's something that we need to take note of and act upon.
"It's an interesting development. It's an opportunity we'll look at today."
City are not the only club thought to be interested in the Lancashire-born ex-Southampton trainee. Charlton, Ipswich and Derby are all thought to have had approaches previously turned down by Colchester, while Preston and Sunderland are also considering him.
But Parkinson's resignation came at a very timely moment, after Peter Taylor's move to Crystal Palace the previous day made the City post available, which could indicate that he is destined for the KC Stadium.
Meanwhile, on his way out could be City's first team coach Steve Butler. He came to City just days after Peter Taylor became manager in October 2002, having previously worked with him at Gillingham and Leicester. He could follow Taylor to Palace, as Pearson expects City's new manager will want to bring in new coaching staff. However, he says that goalkeeping coach Mark Prudhoe and physio Simon Maltby will stay, and assistant manager Colin Murphy may even remain with the club as well.