During the first One-Day International in Bristol, which was eventually abandoned due to rain, Swann ruled out England winning the 2015 World Cup during a commentary stint on the BBC's Test Match Special programme.
"We won't win this World Cup," Swann said. "In four years' time, we might have a chance if we get in all the exciting players who have none of the baggage of the old-style brand we play."
Asked about Cook's position in the team, Swann, who took 104 wickets in 79 ODIs and played at the 2011 World Cup, added:
"I love Cookie dearly, but I don't think he should be bothering playing one-day cricket anymore.
"He doesn't need to. He's proved a very good point in Test matches. He should just enjoy being England Test captain. Let in the young people who just want to smash it everywhere.
"He's not the guy who should be opening the batting in one-day cricket for England. (James) Vince should be doing it with (Alex) Hales in a young vibrant team with Eoin Morgan as captain."
And following England's 133-run defeat to India in the second ODI in Cardiff, Cook had this to say in his post-match press conference.
"I don't think it's that helpful, especially from a so-called friend.
"He's entitled to his opinion, but it's not ideal for me, especially when you get through the summer I've had.
"I am a little bit disappointed because he is a good friend of mine and has been a supporter."
In what has been a difficult summer for Cook, he has also had the likes of Kevin Pietersen, Michael Vaughan and Shane Warne criticise him at different times as he struggled for form with the bat and also came under fire for his leadership.
England turned a 1-0 deficit around to win the Test series 3-1 and now have to the same again as the ODI series moves on to Trent Bridge on Saturday (30th August).
© Cricket World 2014