The war of words between Cook and his former team-mate Swann escalated with the ex-England off-spinner saying "Real mates are honest with each other. Being the one-day captain is a poisoned chalice for him. He just doesn't need the job."
"We're happy to tootle along in a two-litre diesel in a Formula 1 race," Swann told The Sun.
Swann, who took 104 wickets in 79 one-day internationals for England and retired in December, has claimed that Cook "should not bother" with the one-day game.
Swann wants an overhaul of the one-day team before next year's World Cup.
England suffered a 133-run defeat by India in the second one-day international in Cardiff on Wednesday after the first match in Bristol was rained off.
Swann said he was not surprised by the reaction of Cook, 29, who faced calls to quit as Test captain earlier this summer.
"It's never nice when you feel your nose has been put out of joint. I'm sure I'll speak to Cooky over the next couple of days but I won't back down from what I said," Swann said.
Swann feels that Cook's one-day strike rate -- currently at 77.98 runs per 100 balls -- does not set the tone to make England competitive in the World Cup in Australia and New Zealand.
"In one-day matches I want England to play the exciting cricket they promised six months ago when Peter Moores took over as head coach," he said.
"In one-day cricket you should pick your 11 best players and choose your captain from there and I don't think he is one of the best 11 players," Swann added.
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