Roberto Mancini signalled that his striker will be caught in a club-versus-country role by saying it was "impossible" that Aguero, who has a knee injury, could play.
City have earmarked the trip to Stoke city on September 15 for the 24 year old's comeback but Argentina manager Alejandro Sabella wants the forward to face Paraguay on September 7 and Peru four days later.
"It is impossible," Mancini said yesterday. "Sergio needs minimum two weeks without training and maybe two weeks [of training before] he can play again. He can't go." Under Fifa rules, national teams are entitled to use their own doctors to examine players to determine if they actually are unfit to play.
However, in Aguero's case, that would involve a journey of several thousand miles to South America.
"He can go and after [the medical] he can fly back. They are ridiculous rules," Mancini added.
The news about Aguero's call-up has tempered City's joy after discovering that Aguero will return sooner than they had anticipated when he was carried off during Sunday's 3-2 win over Southampton.
"I think we were really lucky with Sergio because it could be a very bad injury," Mancini added.
But City will be without Aguero tomorrow when they travel to Anfield to a Liverpool side missing one of Mancini's major summer transfer targets. Daniel Agger is suspended and will not line up against City and, after Liverpool rejected a bid, he will not join them either. "No chance," Mancini said.
Yet he refused to rule out signing Daniele De Rossi, even though the Italy international insisted he is staying at Roma.
"It is a difficult situation but from my experience, until the [transfer] window is closed, anything can happen," he said.
So far, Everton midfielder Jack Rodwell is City's only summer signing and Mancini has complained that clubs are demanding inflated prices when they come calling.
"For us, the market is more difficult because every club that talked with us started [asking for] £30 or £40 million (Dh232.6m)," he said. "This was not correct."
Without Aguero,Mario Balotellicould be given a first start of the season at Anfield, where he was sent off in a 1-1 draw last November.
The Italian excelled in Euro 2012, where his semi-final brace defeated Germany, and the often controversial striker has contrived to stay out of the headlines recently, prompting questions if he has matured.
"Mario is the same," Mancini said. "I don't think he can change in one month. But if Mario always plays like he played in European Championship, it will be better."
Besides Aguero, City go to Anfield without either Gareth Barry and Micah Richards and with the manager complaining he is down to 19 fit, first-team players.
He is hopeful City can add to their squad in the last month of the transfer window, with Swansea winger Scott Sinclair still a target, but Mancini insisting that he is not interested in Inter right-back Maicon and that Athletic Bilbao's Javi Martinez is overpriced and is reluctant to let players leave unless replacements can be secured.
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