Manchester City attempted to buy the 29-year-old on the final day of the summer transfer window, but Arsenal were forced to turn down the £60 million deal as they could not find a suitable replacement.
Lee added that City are "unwilling" to part with that amount, although according to James Olley of the Evening Standard, Arsenal want even more than the sum quoted, with a valuation of £40 million said to have been placed on Sanchez.
Manchester City are increasingly confident of sealing a move for Arsenal forward Alexis Sanchez during this month's transfer window, sources close to City have told ESPN FC.
The Chile global has entered the final six month of his Gunners contract, and his representative is free to discuss a pre-contract agreement with a foreign side this month.
If true, that would rule him out for the rest of the season, thus increasing the need for City boss Pep Guardiola to sign reinforcements up top with only Sergio Aguero as the club's only fit senior striker.
The report from Goal states: Alexis was left out of the Arsenal squad for their FA Cup third-round tie at Nottingham Forest on Sunday, which the Gunners lost 4-2. Sanchez would strengthen the already frighteningly good City attack, and act as cover whilst Gabriel Jesus recovers.
I understand that Sanchez has again reiterated his desire to leave to Arsenal - and they are now ready to listen, and the player is hopeful that City can strike a deal this month, rather than waiting until the summer, when he can move on a free transfer.
While City are set to coast to the Premier League title-they have a 15-point lead over their nearest rivals-Sanchez would give them a huge boost in the UEFA Champions League.
Theo Walcott is another player who is set to leave Arsenal this month with a return to Southampton a real possibility.
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