Sanchez has been linked to a reunion with his former Barcelona boss Pep Guardiola at the Etihad Stadium throughout the transfer window, with the 28-year-old in the last season of his contract.
Arsenal are understood to have rejected a £50 million offer on Tuesday but, with an improved bid in the region of £70m expected, the Independent reported City have sent a delegation to Chile in anticipation of finalising a club-record deal.
Juan Antonio Pizzi's side are preparing for crunch World Cup qualifiers against Paraguay and Bolivia and La Tercera reported Sanchez might have caused some unwelcome disruption on Wednesday, claiming he asked his coach to be given time off to deal with some "personal formalities".
Speaking at a news conference ahead of Paraguay's visit to the Estadio Monumental David Arellano on Thursday, ex-Valencia boss Pizzi insisted such speculation was wide of the mark.
"No. It's absolutely false. That permission never existed," he said.
"Sometimes players request authorisation for some things and sometimes we grant them and other times we don't.
"I'm against rigid decisions, each case is different. We consider the individual situation of each player regarding many variables.
"But we always take into account that we are in a national team camp."
Arsenal suffered a dispiriting 4-0 defeat to Liverpool on Sunday, with the Merseyside club widely reported to be on the verge of signing Alex Oxlade-Chamberlain from the Gunners.
With the toxic atmosphere of the last season seemingly on the verge of returning to Emirates Stadium, Sanchez's exit could be seen as imperative for the star attacker, but Pizzi is not of this opinion.
"It's very difficult before the transfer window closes to shed light on his future," he said.
"In either option his future is very good. There is no reason to be displeased or dissatisfied. Both options are excellent.
"We are talking about a first-class player, who is coached by one of the best in the world. The conditions he has at Arsenal are spectacular."
Pizzi added: "He's worked well and he is happy. To say that he is nervous about his future is somewhat ironic, anyone would like to have those worries.
"He has the maximum disposition, he is in a good mood to represent the national team."