The Ayrshire club turned down a slightly smaller bid from Oldham for the 25-year-old Northern Ireland striker earlier in the week.
However, this latest offer is being considered by the Rugby Park club as it will involve financial add-ons.
It is understood Charlton are confident a £3,000-a-week package will be enough to secure his signature.
Should Magennis leave for Charlton it would be a blow to Killie boss Lee Clark, since the player has been a key figure in his line-up since he became the manager in February.
Magennis featured as a substitute in all of Northern Ireland's games at Euro 2016.
League One Charlton Athletic have made a bid of £100,000 for Kilmarnock striker Josh Magennis.