The two defenders will cost Everton around £18m and £12m respectively.
The Toffees are reported to have made an offer of £18m for Kone, but Sunderland have not confirmed the offer.
Meanwhile, discussions over the signing of Swansea's Ashley Williams appear to be in more advanced stages. Everton have agreed a fee of £12m for the Swansea skipper and the defender is due to undergo a medical at Goodison Park today.
Williams has reportedly said his goodbyes to his Swansea team-mates and it looks increasingly likely that he will be an Everton player very soon.