Reports have linked Sanchez with a move to Pep Guardiola's side in exchange for England forward Raheem Sterling.
"No formal bid but fair to say that figure was turned down. No player involved," an Arsenalspokesperson said.
There could be an exodus of players from the Emirates before Thursday's transfer deadline with British media reporting that an agreement for Chelsea to sign Alex Oxlade-Chamberlain was close.
But Arsenal said a deal for the 24-year-old England midfielder was not agreed.
"Nothing has moved on with him yet," the spokesperson said.
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