Giunta adds United still need to agree a transfer fee with the Gunners.
Express Sport understands the Red Devils offered £25m for his services, £5m more than rivals City.
But Pep Guardiola, who has been chasing the forward since last summer, now looks set to miss out on his top target.
Arsene Wenger is hopeful of keeping hold of his star man and refused to give much away in his press conference this afternoon when asked about United’s interest.
“I cannot say much more about the situation,” he said.
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Jose Mourinho is keen to bring Alexis Sanchez to Manchester United this month
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“Nothing is concrete at the moment.
“I don’t want to give you wrong information. Nothing is decided.”
When asked about a potential bidding war between City and United, Wenger added: “It is always beneficial to the club who can take advantage.
“I maintain what I have said many times that he should stay until the end of the season. But we will see.”