The 25-year-old had talks with the San Siro outfit over a season-long loan, but his father and agent, Kujtim Mustafi, seems there is no chance of a move materialising by the time the period closes on Thursday.
"I'm his agent and I'm sitting here relaxing at home," told Fussballtransfers.com. "Nothing will happen today."
Mustafi is still contracted to Arsenal until 2021 but has featured just once in the four competitive games they have played this season - a 1-0 defeat to Stoke City.
Arsene Wenger has already seen Wojciech Szczesny, Kieran Gibss and Gabriel Paulista leave this summer, while Alex Oxlade-Chamberlain is set to join Liverpool for £35m.
There is still uncertainty around Alexis Sanchez's future, as the club rejected a £50m offer from Manchester City for the Chile international, but another bid worth around £70m could be made.