Wilshere has been spotted smoking in the past, something which current boss Wenger didn't take too kindly to on the previous occasion, and Graham says that Wenger needs to tell the 22-year-old about the responsibilities he has.
He told TalkSport: “Arsene Wenger is the right man to deal with it. He wants a person to not only train well and eat well, but behave well.
"After the bad publicity shots in the newspapers, somebody has got to have a word with him and I think Arsene Wenger will do.
"His career has not gone anywhere in the last 18 months. The papers now want any sort of publicity of players misbehaving and he has got to get his act together."
Some will look at this being misbehaviour from Wilshere, whilst there will be some wondering what the fuss is about given that Wilshere has yet to report back for pre-season training and is still enjoying some time off.
Wenger will probably frown upon the images because he would prefer his players not to smoke, but some will say that other footballers have had successful careers despite being fond of having the occasional cigarette.
On this occasion, Wilshere hasn't done it whilst he's been back at his club. Given the context of the situation it clearly shows he was on a break, but his manager will not want him indulging in such habits regardless of the situation. The publicity that has come with it, as outlined by Graham, has not been great.