Swansea rejected £40 million bids from both Leicester and the Toffees, as the Welsh side value the Icelandic midfielder at £50 million.
After Swans boss Clement gave his team hope of retaining the 27-year-old, Ronaldo Koeman has showed himself to be optimistic of his signing.
'Everybody knows we are looking for three more players, a left centre-back, a left full-back, a player who can play out of both positions, a winger and a striker and that's the picture, what the best is for our team and we will see what we can do', the Dutch coach told Sky Sports.
'We are close [on Sigurdsson], we have to wait. But still, the deal is not done', Koeman said.