According to Neil Fissler of the Sunday Express, the Serie A side were impressed by the midfielder during the Gunners' 2-0 win at the San Siro in the UEFA Europa League on Thursday and are ready to capitalise on the contract impasse between the player and Arsenal.
Wilshere's Gunners contract is set to expire at the end of this season, meaning he is free to discuss terms with clubs outside of the Premier League with a view to a free transfer in the summer.
Fissler reported that Arsenal have offered the England international £90,000 per week to stay with the club, a drop from the £120,000 per week he will earn until June. According to Fissler, the Milan giants are joined by Juventus and Sampdoria in holding an interest in the 26-year-old.
Few would have anticipated this scenario panning out; not only has Wilshere's career been besieged by injuries in recent years, but he has always held a strong affinity with Arsenal, having come through the club's academy setup.
Wilshere has fought his way back into the side in recent months, and to his credit, he's been able to put together a consistent run of games. As journalist Layth Yousif highlighted, the Italian press were impressed with the midfielder:
Although it's been a season to forget for Arsenal in many respects, Wilshere's renaissance has been a major positive.
The playmaker offers the Gunners something different in the middle of the pitch, as he's able to break the game open with a surging run from deep or through his composure in the final third. There's also an edge to the England man that's in short supply throughout the rest of the Arsenal squad.
Having seen him perform well this term and seemingly put his longstanding fitness issues behind him, it would be galling for Arsenal if their academy graduate did walk away for nothing at the end of the campaign.
Bleacher Report's Dean Jones believes Wilshere has every right to stand his ground in the contract negotiations:
When asked about a prospective new deal recently, the Arsenal No. 10 said he was "no closer" to an agreement with the Gunners, per Ed Malyon of The Independent. And with some big clubs said to be sniffing around the player, there will be some nervousness at the Emirates Stadium about what's to come.
Milan would represent a tempting option too, as Wilshere would be joining one of the most historically significant clubs in football and a team intent on scaling the heights of the game again. Being part of that challenge could tempt the midfielder into starting an exciting new phase of his career.