The Black Cats have agreed a deal with the Merseyside club to sign the Italian forward, who spent last season on loan at the Stadium of Light.
"Fabio wants to stay," Soccerway quotes De Marchi as saying. "His project with Liverpool started two years ago when he left Roma. He began a journey and it is a major project for him.
"He should not be judged on his first year [at Liverpool]. He was out for six months with various injuries and during the past year he took a step back by going to Sunderland and he has had an extraordinary season.
"Now, after the loan, Liverpool have not told me anything. I think he will stay, he is convinced that he will play."
Borini scored 10 goals in 40 appearances for Sunderland last term.