The Us finished second in League One, securing promotion with a goalless draw at Yeovil on the final day of the season.
A statement from the club read: "In view of recent speculation surrounding approaches from other clubs regarding Phil Parkinson, Colchester United can confirm that they have refused permission for three clubs to speak to the manager.
"The Us have refused approaches from Premiership team Charlton Athletic, as well as Championship sides Ipswich Town and Derby County - a position which all three clubs have accepted.
"While recognising that Mr Parkinson must have ambition for the future, it is vital we look to retain him for the future interest of everyone connected with Colchester United at this critical stage.
"Mr Parkinson has been kept fully aware of all developments during this past week."