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.