The two-time Premier League champions were said to have felt confident in securing the 28-year-old's signature after submitting a formal £50m offer on Tuesday.
According to the Daily Mail, City officials were encouraged at around 10am this morning that the Gunners were closing in on a replacement, but communication with the North London outfit became more difficult this afternoon.
It was later revealed that Arsenal's attempts to sign Monaco star Thomas Lemar in a £92m deal fell through amid reports that the midfielder preferred a move to Liverpool because of Champions League on offer.
The Daily Mail reports that City have been left seething at their competitors' conduct, with one newspaper source describing Arsenal as "shambolic".
It is believed that Pep Guardiola's club had members in South America to help carry out the transfer for Sanchez, who is currently overseas on international duty with Chile.
The former Barcelona star will be able to leave Arsenal on a free transfer next summer if he does not sign a new contract.