Pep Guardiola’s side won the Premier League crown in the Spanish head coach’s second season in charge at the Etihad Stadium.
Manchester United finished in second spot but a staggering 19 points behind their derby rivals in the title race.
Tottenham and Liverpool FC secured the final two Champions League qualification spots ahead of Chelsea FC and Arsenal.
Jurgen Klopp’s side earned plenty of praise for their swashbuckling performances in Europe before Liverpool FC lost 3-1 to Real Madrid in the Champions League final.
Tottenham, meanwhile, continued their development under Mauricio Pochettino but Spurs still haven’t won a trophy since the Argentinian coach took over the reins.
Former England international Redknapp believes Liverpool FC and Spurs will push Manchester City in the Premier League title race next term.
“Liverpool and Tottenham will be the closest challengers to Manchester City,” Redknapp told Sky Sports.
“Obviously, Manchester United under Jose Mourinho will want to kick on, but Liverpool and Tottenham will be the closest to City.
“Having said that, I’ve got a feeling City are going to do it again, they’ve got so many good players.”
Manchester United haven’t won the Premier League title since Sir Alex Ferguson stood down as manager at the end of the 2012-13.
The Red Devils have won the FA Cup, the Europa League and the League Cup since the Scot’s retirement.
Manchester United have signed Fred and Diogo Dalot in the summer transfer window so far.
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