Barca saw a 35million euro offer for Fabregas rejected recently but the Catalan giants are likely to up their efforts to bring him back to the Nou Camp following Sunday's presidential elections.
And Keown, who is part of the coaching staff at Arsenal, believes the Gunners will have no choice but to let their captain go.
"Fabregas will certainly leave," said Keown in the Sunday Mirror. "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."
Fabregas learned his trade as a youngster at Barca before moving to the Gunners seven years ago and has made no secret of his desire to return to his hometown club.