The 25-year-old has been working his way back to full fitness after breaking his leg in the closing stages of last season while on loan at Bournemouth.
Wilshere's long-term future remains uncertain as he has just one year left on his current contract at the Emirates, but manager Arsene Wenger recently insisted that he wants the midfielder to stay put.
On Monday evening, the England international stepped up his recovery by featuring for Arsenal's Under-23s in a game against Manchester City, but he lasted just an hour as he was sent off for shoving Matthew Smith after being on the receiving end of a hard tackle.
While scrolling through social media after the game, Wilshere took issue with The Sun's tweet, which read: "Jack Wilshere's career hits new low after shock incident."
The midfielder addressed the journalist by writing: "Evening Sam...Intrigued to hear more about how you think this is a career low for me? Would love a sit down with you? Look forward to it."
Evening Sam...Intrigued to hear more about how you think this is a career low for me? Would love a sit down with you? Look forward to it. https://t.co/nyVzXGyNxA— Jack Wilshere (@JackWilshere) August 22, 2017
Wilshere has not started a league game for Arsenal since the 2015-16 campaign.