The Iceland midfielder finally completed his move to Everton on Wednesday after discussions between the two clubs dragged out all summer.
"I made it clear to Gylfi at the end of last season and conversations I had via texts with him over the summer that I would like him to stay," Clement said.
"His view was that he would like the opportunity to potentially embark on another challenge.
"I was aware of that from the end of last season. The conversations were open and frank, but you still hope there might be a change of mind."