Capello said: "Arnesen wants Van Basten to take over and has already recommended Marco to Abramovich."
Capello added: "Frank and Marco know each other well from their time in Dutch football."
Van Basten, 40, sat behind Abramovich at Old Trafford in Sunday's defeat to Manchester United.
The Dutchman privately insisted it was just a coincidence and that he was a United guest.
Ex-AC Milan hitman Van Basten asked for a few days to decide whether to take the job immediately. A close pal told The Sun: "Marco is faced with a huge dilemma. He has to think things over and see whether he could leave Holland."