There had been speculation that the England Under-21 left back, who is on the transfer list at The Valley, could be targeted by The Saints if Wayne Bridge completed a move to big-spending Chelsea.
However, Andrew Mills insisted that such talk was premature, and that Konchesky had smoothed relations with Charlton following talks with boss Alan Curbishley.
"The Southampton link is one of those things that people put together," said Mills.
"It has not been discussed at length, and I certainly haven't talked to Paul or Alan (Curbishley) about it.
"Until something official actually happens there's very little you can say about it.
"I think Paul has come to a compromise since he spoke to Curbishley about his situation."
Konchesky had asked to be placed on the Addicks' transfer list earlier in the summer after claiming that being played out of his favoured left back role was damaging his England ambitions.
It now seems that the 22-year-old is set to remain with Charlton for whom he has already made over 100 appearances.
