Keown, an ex-Arsenal stalwart and hardman turned pundit, has reigning champions Leicester City missing out, along with the previous winners Chelsea, and Jurgen Klopp's Liverpool.
Here are Keown's predictions: 1) Manchester City, 2) Manchester United 3) Arsenal 4) Tottenham.
His prediction would see his former side Arsenal maintain their immaculate record under Arsene Wenger of always finishing in the top four and qualifying for the Champions League, and above bitter North London rivals Tottenham.
Arsenal manager Arsene Wenger and his assistant Steve Bould
He added a piece of good news for Liverpool fans - that he tips them to win this season's FA Cup.
Liverpool came close to winning the League Cup and Europa League last season, defeated in both finals.
This year's Premier League looks like being one of the most difficult to predict, but last year it seemed like a certainty between Chelsea, Manchester City or Arsenal ahead of the campaign - three teams which blew their chances and saw surprise package Leicester City stun everybody.
Leicester City's Danny Drinkwater, Jamie Vardy and Robert Huth with the trophy on the bus during the parade