Manchester United have been linked with a potential move to sign the German midfielder in the January transfer window or perhaps for nothing next summer.
While Arsene Wenger has repeatedly insisted neither Sanchez nor Mesut Ozil, who is also out of contract at the end of the season, will be allowed to leave in January, City believe the Gunners' boss can be persuaded to accept a bid in the winter transfer window.
The Chilean forward may be a brilliant player, but even in a world of petrodollar fuelled clubs and television deals worth billions, such a fee would be surprising considering he is available for nothing in a few months.
The two clubs had finally agreed a deal on summer transfer deadline day, only for Arsenal to pull out when negotiations for a possible replacement in Monaco's Thomas Lemar broke down.
Emmanuel Petit is praising the current form of the forwards, whilst asking the question as to the reasoning for the recent performances.
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We were fourth seeds in this and over the Champions Leauge there won't be too many of those who have jumped up to third place and gone through.
According to the report, Guardiola feels the foundations have been built to mount a challenge on the Premier League and UEFA Champions League crowns this term, and Sanchez would add a key piece of quality to the squad.
Roma sporting director Monchi has revealed in the past his admiration for Vazquez, 26, but the Italian outfit will need to make a firm bid for Real to consider selling and then swooping for Sanchez as an alternative in January.
Many pundits wonder why Guardiola is so desperate to sign Sanchez.