The Gunners turned down a move from the Spanish giants earlier this month.
Keown told the Sunday Mirror: “Fabregas will certainly leave. What we are seeing at the moment are long, protracted, drawn-out negotiations between Arsenal and Barca.
“Arsenal are showing their early position and Barcelona are looking to get him for as cheap as they can.
“If Fabregas’ body language is wrong, he’s such an important figure, then he has to go. We trust in Wenger to make the right decision for the football club.
“The move to Barcelona is something that has been in his mind for some time. He wants to go back to where he began, but at the same time he wants to be respectful to Arsenal and to Arsene who has nurtured him through.
“It must have been difficult for him to see Arsene Wenger and ask for the move.”