The Toffees finally landed Sigurdsson earlier this week following drawn-out negotiations for the Icelandic midfielder, which eventually culminated in a £45m move for the 27-year-old.
"I spoke to the owners last night and what we will do moving forward," Clement told reporters ahead of the club's coming Premier League fixture with Manchester United.
"We have received a good transfer fee and funds are available to strengthen the squad.
"It is a big challenge replacing Gylfi, but I hope we can potentially bring in two or three players to strengthen us in various positions."
The Swans opened their new league campaign with a goalless draw away at Southampton last weekend.