"The latest offer from Everton has been rejected," his agent Jim McArthur told skysports.com. "The offer was rejected last week before Gary went away on international duty with Scotland. As far as I am concerned things are ongoing, but I have not spoken to anyone from Everton since the latest offer.
"Gary is keeping his options open and one of them is Everton and anyway nothing could happen until January."
Everton clearly want naysmith to stay, but i suspect he is concerned that his lack of first team action will put his Scotland place in question, and with Celtic clearly interested in him, it looks unlikely that he will stay beyond January.