The Addicks, who have been relegated to League One, made a move for Wilder after Jose Rigaannounced his departure following the club's final game of the Championship season at the weekend.
However, after early discussions with Wilder and his assistant Alan Knill, Charlton have opted to consider other candidates.
A statement from the club read: "Charlton Athletic can confirm that following discussions with Northampton Town manager Chris Wilder and his assistant Alan Knill over the vacant managerial role at The Valley, the club has been unable to reach an agreement.
"The club will now continue its search for a candidate to take the club forward. Any further announcements will be made in due course."
Wilder and his Northampton team secured the League Two title this season.