The former Whites and Newcastle man helped the Addicks achieve promotion to the Championship via the play-offs in his first full season at the club.
However, with the club up for sale, current owner Roland Duchatelet was unwilling to offer Bowyer any longer than a 12-month extension, leading to an impasse.
A statement on Charlton's website read: "Charlton Athletic have been unable to reach an agreement with manager Lee Bowyer regarding the extension of his contract.
"The fact the club is for sale has not helped with finding an agreement. The current owner needs to take into account that a new owner may want to appoint his own manager.
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"However, this concern did not stop the current owner proposing a contract extension of one year to Lee Bowyer, even though the club may be sold in a few weeks. Under those circumstances a multi-year extension would not be good business practice."
The statement continued: "In addition, since the club is still losing money, which is one of the reasons why the club has not been sold yet, the focus on reducing costs means that we are extremely limited on payroll increases.
"Lee has been offered a one-year extension to his contract at a level which is approximately three times what he had since his last increase when he became permanent manager in September.
"This reflects the strong desire we have to continue to have Lee as our manager. But Lee wanted much more.
"Unlike previous contract discussions, Lee wanted an agent to handle it. We reluctantly accepted. However, involving a player agent in a manager's contract discussion is not healthy."
The statement concluded: "The club hasn't started to look for any other manager in the meantime and does not intend to appoint a permanent manager, since the club is going to be sold.
"A caretaker manager will be announced in due course and in the meantime the other staff members will continue to prepare for the upcoming season for which a lot of good work has been performed already.
"If Lee does change his mind before his contract expires and chooses to continue his good work at Charlton, he is still welcome to stay.
"However our ability to sell the club is the most important thing right now."